Cyclotomic numbers and Chebyshev polynomials

introduction

• borrowed from Andrews-Gordon identity
• quantum dimension and there recurrence relation
  \(d_i=\frac{\sin \frac{(i+1)\pi}{k+2}}{\sin \frac{\pi}{k+2}}}\) satisfies
  \(d_i^2=1+d_{i-1}d_{i+1}\) where \(d_0=1\), \(d_k=1\)
  

 

1. (*choose k for c (2,k+2) minimal model*)k := 11
   d[k_, i_] := Sin[(i + 1) Pi/(k + 2)]/Sin[Pi/(k + 2)]
   Table[{i, d[k, i]}, {i, 1, k}] // TableForm
   Table[{i, N[(d[k, i])^2 - (1 + d[k, i - 1]*d[k, i + 1]), 10]}, {i, 1,
      k}] // TableForm
   
2. Plot[d[k, i], {i, 0, 2 k}]
   

 

 

cyclotomic numbers

• Gauss sums
• 원분다항식(cyclotomic polynomial)
• character tables of finite groups
• values of Lie group characters at elements of finite order
• matrix entries in the modular group representation coming from rational VOAs
  
  • Kac-Peterson modular S-matrix
• quantum dimension in RCFT
• fusion rules and Verlinde formula
• Jones index ofsubfactors

 

 

chebyshev polynomials

• 체비셰프 다항식
• http://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html
  also obey the interesting determinant identity
  
  

 

 

history

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

 

 

 

 

encyclopedia

• http://ko.wikipedia.org/wiki/
• 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=

 

 

articles

 

• 논문정 리
• http://www.ams.org/mathscinet
• http://www.zentralblatt-math.org/zmath/en/
• http://pythagoras0.springnote.com/
• http://math.berkeley.edu/~reb/papers/index.html
• 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
• 수식표 현 안내
• The On-Line Encyclopedia of Integer Sequences