"Complex reflection groups"의 두 판 사이의 차이

수학노트
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(사용자 3명의 중간 판 29개는 보이지 않습니다)
1번째 줄: 1번째 줄:
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<h5>간단한 소개</h5>
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==introduction==
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* arrangement of hyperplanes
  
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<h5>관련된 학부 과목과 미리 알고 있으면 좋은 것들</h5>
 
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<h5>관련된 대학원 과목</h5>
 
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<h5>관련된 다른 주제들</h5>
 
  
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==related items==
 
* [[01 thesis|Hypergeometric series]]
 
* [[01 thesis|Hypergeometric series]]
  
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<h5>표준적인 도서 및 추천도서</h5>
 
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* http://search.gigapedia.com/?q=
 
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* http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
 
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<h5>위키링크</h5>
 
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* http://en.wikipedia.org/wiki/
 
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<h5>참고할만한 자료</h5>
 
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On Coxeter Diagrams of complex reflection groups
 
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Authors:[http://arxiv.org/find/math/1/au:+Basak_T/0/1/0/all/0/1 Tathagata Basak]
 
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http://arxiv.org/abs/0809.2427
 
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'''Title:''' The complex Lorentzian Leech lattice and the bimonster'''Authors:''' Tathagata [http://front.math.ucdavis.edu/author/T.Basak Basak]
 
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http://front.math.ucdavis.edu/0508.5228
 
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'''Title:''' The complex Lorentzian Leech lattice and the bimonster (II)
 
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'''Authors:''' Tathagata [http://front.math.ucdavis.edu/author/T.Basak Basak]
 
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http://front.math.ucdavis.edu/0811.0062
 
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Regular polyhedral groups and reflection groups of rank four
 
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'''Mitsuo Kato [[mailto:mkato@edu.u-ryukyu.ac.jp]]<sup>,</sup>[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WDY-4B0WHXW-1&_user=4420&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000059607&_version=1&_urlVersion=0&_userid=4420&md5=188db4d982dbbcd13fb099e37f43bc91#aff1 a] and Jiro Sekiguchi [[mailto:sekiguti@cc.tuat.ac.jp]]<sup>,</sup>[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WDY-4B0WHXW-1&_user=4420&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000059607&_version=1&_urlVersion=0&_userid=4420&md5=188db4d982dbbcd13fb099e37f43bc91#aff2 b]'''
 
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http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WDY-4B0WHXW-1&_user=4420&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000059607&_version=1&_urlVersion=0&_userid=4420&md5=188db4d982dbbcd13fb099e37f43bc91
 
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26 Implies the Bimonster[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WH2-45B5NX1-K&_user=4420&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000059607&_version=1&_urlVersion=0&_userid=4420&md5=e01e884479d443f48357724a9b672e9f#m4.1 *1]
 
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'''John H. Conway[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WH2-45B5NX1-K&_user=4420&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000059607&_version=1&_urlVersion=0&_userid=4420&md5=e01e884479d443f48357724a9b672e9f#a1 a]<sup>,</sup>[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WH2-45B5NX1-K&_user=4420&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000059607&_version=1&_urlVersion=0&_userid=4420&md5=e01e884479d443f48357724a9b672e9f#fn1 1] and Christopher S. Simons[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WH2-45B5NX1-K&_user=4420&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000059607&_version=1&_urlVersion=0&_userid=4420&md5=e01e884479d443f48357724a9b672e9f#a2 b]<sup>,</sup>[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WH2-45B5NX1-K&_user=4420&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000059607&_version=1&_urlVersion=0&_userid=4420&md5=e01e884479d443f48357724a9b672e9f#fn2 2]'''
 
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http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WH2-45B5NX1-K&_user=4420&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000059607&_version=1&_urlVersion=0&_userid=4420&md5=e01e884479d443f48357724a9b672e9f
 
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<h5>수식표현템플릿</h5>
 
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수식을 입력하고 싶으면, 아래와 같은 형식의 이미지 주소를 작성, '삽입'->'이미지 첨부'->'외부 URL로 첨부하기' 를 선택. (powered by MIMETEX)
 
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수식의 구조는 http://bomber0.byus.net/mimetex/mimetex.cgi? + LaTeX 명령어
 
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LaTeX 명령어 테스트는 http://www.forkosh.dreamhost.com/source_mimetex.html#preview 에서 할 수 있음.
 
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http://www.sitmo.com/latex/ 에서 수식 이미지를 복사해서 붙여 넣어도 됨. 위 방법과 동일하게 LaTeX 기반.
 
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수식 이미지 복사는 인터넷 익스플로러에서는 일단 가능한데, 파이어폭스 등의 기타 브라우저에서는 잘 안 되네요. 참고하세요.
 
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LaTeX 명령예
 
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* <math>x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math>
 
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# x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
 
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* <math>e^{i \pi} +1 = 0</math>
 
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# e^{i\pi}+1=0
 
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* <math>2\pi-3\times\frac{3\pi}{5}=\frac{\pi}{5}</math>
 
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# 2\pi-3\times\frac{3\pi}{5}=\frac{\pi}{5}
 
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* <math>\frac{\sqrt{3}}{5}</math>
 
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# \frac{\sqrt{3}}{5}
 
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* <math>720\div12=60</math>
 
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# 720\div12=60
 
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* <math>\large f^\prime(x)\ =        \lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x}</math>
 
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# \large f^\prime(x)\ =         \lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x}
 
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* <math>\Large A\ =\ \large\left(        \begin{array}{c.cccc}&1&2&\cdots&n\\        \hdash1&a_{11}&a_{12}&\cdots&a_{1n}\\        2&a_{21}&a_{22}&\cdots&a_{2n}\\        \vdots&\vdots&\vdots&\ddots&\vdots\\        n&a_{n1}&a_{n2}&\cdots&a_{nn}\end{array}\right)</math>
 
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# \Large A\ =\ \large\left(         \begin{array}{c.cccc}&1&2&\cdots&n\\         \hdash1&a_{11}&a_{12}&\cdots&a_{1n}\\         2&a_{21}&a_{22}&\cdots&a_{2n}\\         \vdots&\vdots&\vdots&\ddots&\vdots\\         n&a_{n1}&a_{n2}&\cdots&a_{nn}\end{array}\right)
 
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* <math>\LARGE\tilde y=\left\{ {\ddot x\text{ if $\vec x$ odd}\atop\hat{\,\bar x+1}\text{ if even}}\right.</math>
 
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# \LARGE\tilde y=\left\{  {\ddot x\text{ if $\vec x$ odd}\atop\hat{\,\bar x+1}\text{ if even}}\right.
 
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* <math>\Large\left.\begin{eqnarray}    x+y+z&=&3\\2y&=&x+z\\2x+y&=&z\end{eqnarray}\right\}</math>
 
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# \Large\left.\begin{eqnarray}    x+y+z&=&3\\2y&=&x+z\\2x+y&=&z\end{eqnarray}\right\}
 
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* <math>\int e^{-\frac{x^2}{2}} dx</math>
 
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# \int%20e^{-\frac{x^2}{2}}%20dx
 
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<math>e^x=\lim_{n\to\infty} \left(1+\frac~xn\right)^n</math>
 
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# e^x=\lim_{n\to\infty} \left(1+\frac~xn\right)^n
 
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* <math>\Large\begin{array}{rccclBCB}    &f&\longr[75]^{\alpha:{\normalsize f\rightar~g}}&g\\    \large\gamma&\longd[50]&&\longd[50]&\large\gamma\\    &u&\longr[75]_\beta&v\end{array}</math>
 
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# \Large\begin{array}{rccclBCB}    &f&\longr[75]^{\alpha:{\normalsize f\rightar~g}}&g\\    \large\gamma&\longd[50]&&\longd[50]&\large\gamma\\    &u&\longr[75]_\beta&v\end{array}
 
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* <math>\Large\overbrace{a,...,a}^{\text{k a^,s}},    \underbrace{b,...,b}_{\text{l b^,s}}\hspace{10}    \large\underbrace{\overbrace{a...a}^{\text{k a^,s}},    \overbrace{b...b}^{\text{l b^,s}}}_{\text{k+l elements}}</math>
 
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# \Large\overbrace{a,...,a}^{\text{k a^,s}},    \underbrace{b,...,b}_{\text{l b^,s}}\hspace{10}    \large\underbrace{\overbrace{a...a}^{\text{k a^,s}},    \overbrace{b...b}^{\text{l b^,s}}}_{\text{k+l elements}}
 
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* <math>\normalsize        \left(\large\begin{array}{GC+23}        \varepsilon_x\\\varepsilon_y\\\varepsilon_z\\\gamma_{xy}\\        \gamma_{xz}\\\gamma_{yz}\end{array}\right)\ {\Large=}        \ \left[\begin{array}{CC}        \begin{array}\frac1{E_{\fs{+1}x}}        &-\frac{\nu_{xy}}{E_{\fs{+1}x}}        &-\frac{\nu_{\fs{+1}xz}}{E_{\fs{+1}x}}\\        -\frac{\nu_{yx}}{E_y}&\frac1{E_{y}}&-\frac{\nu_{yz}}{E_y}\\        -\frac{\nu_{\fs{+1}zx}}{E_{\fs{+1}z}}&        -\frac{\nu_{zy}}{E_{\fs{+1}z}}        &\frac1{E_{\fs{+1}z}}\end{array} & {\LARGE 0} \\        {\LARGE 0} & \begin{array}\frac1{G_{xy}}&&\\        &\frac1{G_{\fs{+1}xz}}&\\&&\frac1{G_{yz}}\end{array}        \end{array}\right]        \ \left(\large\begin{array}        \sigma_x\\\sigma_y\\\sigma_z\\\tau_{xy}\\\tau_{xz}\\\tau_{yz}        \end{array}\right)</math>
 
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# \normalsize         \left(\large\begin{array}{GC+23}         \varepsilon_x\\\varepsilon_y\\\varepsilon_z\\\gamma_{xy}\\         \gamma_{xz}\\\gamma_{yz}\end{array}\right)\ {\Large=}         \ \left[\begin{array}{CC}         \begin{array}\frac1{E_{\fs{+1}x}}         &-\frac{\nu_{xy}}{E_{\fs{+1}x}}         &-\frac{\nu_{\fs{+1}xz}}{E_{\fs{+1}x}}\\         -\frac{\nu_{yx}}{E_y}&\frac1{E_{y}}&-\frac{\nu_{yz}}{E_y}\\         -\frac{\nu_{\fs{+1}zx}}{E_{\fs{+1}z}}&         -\frac{\nu_{zy}}{E_{\fs{+1}z}}         &\frac1{E_{\fs{+1}z}}\end{array} & {\LARGE 0} \\         {\LARGE 0} & \begin{array}\frac1{G_{xy}}&&\\         &\frac1{G_{\fs{+1}xz}}&\\&&\frac1{G_{yz}}\end{array}         \end{array}\right]         \ \left(\large\begin{array}         \sigma_x\\\sigma_y\\\sigma_z\\\tau_{xy}\\\tau_{xz}\\\tau_{yz}         \end{array}\right)
 
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==books==
  
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# \sum_{k=1}^{\infty}\frac{1}{k^2}=\frac{\pi^2}{6}
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* Hiller, Howard <em style="">Geometry of Coxeter groups.</em> Research Notes in Mathematics, 54. Pitman (Advanced Publishing Program), Boston, Mass.-London, 1982. iv+213 pp.
  
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*
 
  
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# \int_{a}^{b}f(x)dx=F(b)-F(a)
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==encyclopedia==
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* http://en.wikipedia.org/wiki/Complex_reflection_group
  
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*
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# \exists c \in (a,b) \quad \mathbf{s.t.} \quad f'(c)=\frac{f(b)-f(a)}{b-a}
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==expositions==
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* Shoji, Toshiaki. “Springer Correspndence for Complex Reflection Groups.” arXiv:1511.03353 [math], November 10, 2015. http://arxiv.org/abs/1511.03353.
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* Cohen, Arjeh M. ‘Finite Complex Reflection Groups’. Annales Scientifiques de l’École Normale Supérieure 9, no. 3 (1976): 379–436. http://www.numdam.org/numdam-bin/fitem?id=ASENS_1976_4_9_3_379_0 Finite complex reflection groups
  
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# E=-N\frac{d\Phi}{dt}
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==articles==
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* Ivan Marin, Homology computations for complex braid groups II, arXiv:1605.06953 [math.GR], May 23 2016, http://arxiv.org/abs/1605.06953
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* Robert Laugwitz, On Fomin--Kirillov Algebras for Complex Reflection Groups, arXiv:1605.00227 [math.QA], May 01 2016, http://arxiv.org/abs/1605.00227
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* Gaiffi, Giovanni. ‘Exponential Formulas for Models of Complex Reflection Groups’. arXiv:1507.02090 [math], 8 July 2015. http://arxiv.org/abs/1507.02090.
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* Kosuda, Masashi, and Manabu Oura. ‘Centralizer Algebras of the Primitive Unitary Reflection Group of Order <math>96</math>’. arXiv:1505.00318 [math], 2 May 2015. http://arxiv.org/abs/1505.00318.
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* Schwartz, Richard Evan. “Complex Hyperbolic Triangle Groups.” arXiv:math/0304268, April 18, 2003. http://arxiv.org/abs/math/0304268.
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* <cite class="" id="CITEREFBrou.C3.A9MalleRouquier1995" style="font-style: normal;">Broué, Michel; Malle, Gunter; Rouquier, Raphaël (1995), [http://www.maths.leeds.ac.uk/%7Erouquier/papers/banff.pdf "On complex reflection groups and their associated braid groups"], <em style="">Representations of groups (Banff, AB, 1994)</em>, CMS Conf. Proc., '''16''', Providence, R.I.: [http://en.wikipedia.org/wiki/American_Mathematical_Society American Mathematical Society], pp. 1–13, [http://en.wikipedia.org/wiki/Mathematical_Reviews MR][http://www.ams.org/mathscinet-getitem?mr=1357192 1357192], [http://www.maths.leeds.ac.uk/%7Erouquier/papers/banff.pdf http://www.maths.leeds.ac.uk/~rouquier/papers/banff.pdf]</cite>
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* <cite class="" id="CITEREFBrou.C3.A9MalleRouquier1998" style="font-style: normal;">Broué, Michel; Malle, Gunter; Rouquier, Raphaël (1998), "[http://citeseer.ist.psu.edu/cache/papers/cs/14118/http:zSzzSzwww.math.jussieu.frzSz%7ErouquierzSzpreprintszSzbrmaro.pdf/complex-reflection-groups-braid.pdf Complex reflection groups, braid groups, Hecke algebras]", <em style="">[http://en.wikipedia.org/wiki/Journal_f%C3%BCr_die_reine_und_angewandte_Mathematik Journal für die reine und angewandte Mathematik]</em>'''500''': 127–190, [http://en.wikipedia.org/wiki/Mathematical_Reviews MR][http://www.ams.org/mathscinet-getitem?mr=1637497 1637497], [http://en.wikipedia.org/wiki/International_Standard_Serial_Number ISSN][http://worldcat.org/issn/0075-4102 0075-4102], [http://citeseer.ist.psu.edu/cache/papers/cs/14118/http:zSzzSzwww.math.jussieu.frzSz%7ErouquierzSzpreprintszSzbrmaro.pdf/complex-reflection-groups-braid.pdf http://citeseer.ist.psu.edu/cache/papers/cs/14118/http:zSzzSzwww.math.jussieu.frzSz~rouquierzSzpreprintszSzbrmaro.pdf/complex-reflection-groups-braid.pdf]</cite>
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* Smith, Larry. “On the Invariant Theory of Finite Pseudo Reflection Groups.” Archiv Der Mathematik 44, no. 3 (March 1985): 225–28. doi:10.1007/BF01237854 http://www.springerlink.com/content/km47220t175l6652/
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* <cite class="" id="CITEREFDeligne1972" style="font-style: normal;">[http://en.wikipedia.org/wiki/Pierre_Deligne Deligne, Pierre] (1972), "Les immeubles des groupes de tresses généralisés", <em style="">[http://en.wikipedia.org/wiki/Inventiones_Mathematicae Inventiones Mathematicae]</em>'''17''': 273–302, [http://en.wikipedia.org/wiki/Digital_object_identifier doi]:[http://dx.doi.org/10.1007%2FBF01406236 10.1007/BF01406236], [http://en.wikipedia.org/wiki/Mathematical_Reviews MR][http://www.ams.org/mathscinet-getitem?mr=0422673 0422673], [http://en.wikipedia.org/wiki/International_Standard_Serial_Number ISSN][http://worldcat.org/issn/0020-9910 0020-9910]</cite>
  
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[[분류:개인노트]]
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[[분류:math and physics]]
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[[분류:math]]
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[[분류:Hecke algebra]]
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[[분류:migrate]]
  
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# \mathbf{X}=\left(\begin{array}{ccc}x_{11} & x_{12} & \ldots } & x_{22} & \ldots  & \vdots & \ddots\end{array} \right)
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==메타데이터==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q5156596 Q5156596]
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===Spacy 패턴 목록===
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* [{'LOWER': 'complex'}, {'LOWER': 'reflection'}, {'LEMMA': 'group'}]

2021년 2월 17일 (수) 03:02 기준 최신판

introduction

  • arrangement of hyperplanes



related items


books

  • Hiller, Howard Geometry of Coxeter groups. Research Notes in Mathematics, 54. Pitman (Advanced Publishing Program), Boston, Mass.-London, 1982. iv+213 pp.


encyclopedia



expositions

articles

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'complex'}, {'LOWER': 'reflection'}, {'LEMMA': 'group'}]
원본 주소 "https://wiki.mathnt.net/index.php?title=Complex_reflection_groups&oldid=51886"