Degrees and exponents

introduction

• eigenvalues of Cartan matrices
  
• eigenvalues of incidence matrices of Dynkin diagram
  

 

[1]

 

 

Cartan matrix

• h : Coxeter number
  
• eigenvalue
  \(4\sin^2(\frac{l_n\pi}{2h})\)
  

 

 

adjacency matrix

• h : Coxeter number
  
• eigenvalue \(2\cos(\pi l_n/h)\)
  

 

1. Table[Simplify[2 Cos[Pi*l/5]], {l, 1, 4}]
   Table[Simplify[4 Sin[Pi*l/10]^2], {l, 1, 4}]

 

 

 

 

history

• http://www.google.com/search?hl=en&tbs=tl:1&q=

 

 

 

 

encyclopedia

• http://ko.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/Coxeter_number
• http://en.wikipedia.org/wiki/
• Princeton companion to mathematics(Companion_to_Mathematics.pdf)

 

 

books

 

• 2010년 books and articles
  
• http://gigapedia.info/1/
• http://gigapedia.info/1/
• http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=

[[4909919|]]

 

 

articles

 

• 논문정리
• http://www.ams.org/mathscinet
• http://www.zentralblatt-math.org/zmath/en/
• http://pythagoras0.springnote.com/
• http://math.berkeley.edu/~reb/papers/index.html[2]
• http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
• 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=
• http://dx.doi.org/

 

 

question and answers(Math Overflow)

• http://mathoverflow.net/search?q=
• http://mathoverflow.net/search?q=

 

 

blogs

• 구글 블로그 검색
  
  • http://blogsearch.google.com/blogsearch?q=
  • http://blogsearch.google.com/blogsearch?q=

 

 

experts on the field

• http://arxiv.org/

 

 

links

• Detexify2 - LaTeX symbol classifier
• 수식표현 안내
• The On-Line Encyclopedia of Integer Sequences
• http://functions.wolfram.com/