"Finite dimensional representations of Sl(2)"의 두 판 사이의 차이

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4번째 줄: 4번째 줄:
  
 
<math>p_i(z)=\frac{w^{i+1}-w^{-i-1}}{w-w^{-1}}</math> for <math> i=1,\cdots, k</math>
 
<math>p_i(z)=\frac{w^{i+1}-w^{-i-1}}{w-w^{-1}}</math> for <math> i=1,\cdots, k</math>
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solution for Nahm's equation is 
 
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<math>x_i=1-\frac{1}{p_i(z)^2}</math>.
 
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This gives rise to <math>\varphi(2k+3)/2</math> solutions, on which the Galois group acts simply transitively.
 
  
 
 
 
 
48번째 줄: 40번째 줄:
  
 
* [[cyclotomic numbers and Chebyshev polynomials]]
 
* [[cyclotomic numbers and Chebyshev polynomials]]
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* [[Weyl-Kac character formula]]
  
 
 
 
 

2010년 4월 4일 (일) 15:41 판

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 \( i=1,\cdots, k\)

 

 

  • \(U_{n+1}(x) & = 2xU_n(x) - U_{n-1}(x)\)

 

 

recurrence relation
  • \(p_{0}(z)=1\)
  • \(p_{1}(z)=z\)
  • \(p_i(z)^2=1+p_{i-1}(z)p_{i+1}(z)\)

 

 

 

 

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[[2010년 books and articles|]]

 

 

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