Finite dimensional representations of Sl(2)

introduction

• affine sl(2)
• quantum sl(2)
• 틀:수학노트

 

Clebsch-Gordan coefficients

• 3j symbol (Clebsch-Gordan coefficient)

 

 

Catalan numbers

• http://qchu.wordpress.com/2010/03/07/walks-on-graphs-and-tensor-products/
• http://mathoverflow.net/questions/17197/how-does-this-relationship-between-the-catalan-numbers-and-su2-generalize

1. f[n_] := Integrate[(2 Cos[Pi*x])^n*2 (Sin[Pi*x])^2, {x, 0, 1}]
   Table[Simplify[f[2 k]], {k, 1, 10}]
   Table[CatalanNumber[n], {n, 1, 10}]

 

 

 

history

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

 

 

related items

• affine sl(2)
• Weyl-Kac character formula
• Macdonald constant term conjecture

 

 

encyclopedia

• q-이항정리
• 체비셰프 다항식

 

 

articles

• Bacry, Henri. 1987. “SL(2,C), SU(2), and Chebyshev Polynomials.” Journal of Mathematical Physics 28 (10) (October 1): 2259–2267. doi:10.1063/1.527759.