Cyclotomic numbers and Chebyshev polynomials
http://bomber0.myid.net/ (토론)님의 2010년 4월 2일 (금) 18:18 판
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 \(d_0=1\), \(d_k=1\)
- (*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 - Plot[d[k, i], {i, 0, 2 k}]
cyclotomic numbers
- Gauss sums
- character tables of finite groups
- values of Lie group characters at elements of finite order
- quantum dimensionsin RCFT
- matrix entries in the modular group representation coming from rational VOAs
- Jones index of subfactors
- fusion rules and Verlinde formula
- 원분다항식(cyclotomic polynomial)
chebyshev polynomials
- 체비셰프 다항식
- http://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html
also obey the interesting determinant identity
history
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)
blogs
experts on the field