"Finite dimensional representations of Sl(2)"의 두 판 사이의 차이

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<h5>introduction</h5>
  
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Define <math>w^{2(2k+3)}=1</math> and <math>z=w+w^{-1}</math>
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<math>p_i(z)=\frac{w^{i+1}-w^{-i-1}}{w-w^{-1}}</math> for <math> i=1,\cdots, k</math>
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solution for Nahm's equation is 
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<math>x_i=1-\frac{1}{p_i(z)^2}</math>.
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This gives rise to <math>\varphi(2k+3)/2</math> solutions, on which the Galois group acts simply transitively.
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* <math>U_{n+1}(x) & = 2xU_n(x) - U_{n-1}(x)</math>
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<h5>recurrence relation</h5>
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* <math>p_{0}(z)=1</math>
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* <math>p_{1}(z)=z</math>
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* <math>p_i(z)^2=1+p_{i-1}(z)p_{i+1}(z)</math>
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<h5>history</h5>
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* http://www.google.com/search?hl=en&tbs=tl:1&q=
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<h5>related items</h5>
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* [[cyclotomic numbers and Chebyshev polynomials]]
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<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103);">encyclopedia</h5>
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* http://en.wikipedia.org/wiki/
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* http://www.scholarpedia.org/
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* Princeton companion to mathematics([[2910610/attachments/2250873|Companion_to_Mathematics.pdf]])
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<h5>books</h5>
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* [[2010년 books and articles]]<br>
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* http://gigapedia.info/1/
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* http://gigapedia.info/1/
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* http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
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<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103);">articles</h5>
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[[2010년 books and articles|]]
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* http://www.ams.org/mathscinet
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* http://www.zentralblatt-math.org/zmath/en/
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* http://pythagoras0.springnote.com/
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* [http://math.berkeley.edu/%7Ereb/papers/index.html http://math.berkeley.edu/~reb/papers/index.html]
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* http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
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* http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
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* http://dx.doi.org/
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<h5>question and answers(Math Overflow)</h5>
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* http://mathoverflow.net/search?q=
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* http://mathoverflow.net/search?q=
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<h5>blogs</h5>
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*  구글 블로그 검색<br>
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** http://blogsearch.google.com/blogsearch?q=
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** http://blogsearch.google.com/blogsearch?q=
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<h5>experts on the field</h5>
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* http://arxiv.org/
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<h5>links</h5>
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* [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier]
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* [http://pythagoras0.springnote.com/pages/1947378 수식표 현 안내]
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* [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences]
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* http://functions.wolfram.com/

2010년 4월 4일 (일) 14:15 판

introduction

Define \(w^{2(2k+3)}=1\) and \(z=w+w^{-1}\)

\(p_i(z)=\frac{w^{i+1}-w^{-i-1}}{w-w^{-1}}\) for \( i=1,\cdots, k\)

 

solution for Nahm's equation is 

\(x_i=1-\frac{1}{p_i(z)^2}\).

This gives rise to \(\varphi(2k+3)/2\) solutions, on which the Galois group acts simply transitively.

 

 

  • \(U_{n+1}(x) & = 2xU_n(x) - U_{n-1}(x)\)

 

 

recurrence relation
  • \(p_{0}(z)=1\)
  • \(p_{1}(z)=z\)
  • \(p_i(z)^2=1+p_{i-1}(z)p_{i+1}(z)\)

 

 

 

 

history

 

 

related items

 

 

encyclopedia

 

 

books

 

 

 

articles

[[2010년 books and articles|]]

 

 

question and answers(Math Overflow)

 

 

blogs

 

 

experts on the field

 

 

links
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