Finite dimensional representations of Sl(2)

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

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

 

 

related items

• cyclotomic numbers and Chebyshev polynomials

 

 

encyclopedia

• http://en.wikipedia.org/wiki/
• http://www.scholarpedia.org/
• 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

[[2010년 books and articles|]]

• 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
• http://functions.wolfram.com/