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

수학노트
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<h5>introduction</h5>
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==introduction==
  
Define <math>w^{2(2k+3)}=1</math> and <math>z=w+w^{-1}</math>
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* [[affine sl(2)]]
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* [[quantum sl(2)]]
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* [[Macdonald constant term conjecture]]
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* {{수학노트|url=리대수 sl(2,C)의 유한차원 표현론}}
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<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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==Catalan numbers==
  
 
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* http://qchu.wordpress.com/2010/03/07/walks-on-graphs-and-tensor-products/
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* http://mathoverflow.net/questions/17197/how-does-this-relationship-between-the-catalan-numbers-and-su2-generalize
  
solution for Nahm's equation is 
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# 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}]
  
<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.
 
  
 
 
  
 
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[[분류:개인노트]]
 
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[[분류:math and physics]]
* <math>U_{n+1}(x) & = 2xU_n(x) - U_{n-1}(x)</math>
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[[분류:Lie theory]]
 
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[[분류:migrate]]
 
 
 
 
 
 
 
 
<h5>recurrence relation</h5>
 
 
 
* <math>p_{0}(z)=1</math>
 
* <math>p_{1}(z)=z</math>
 
* <math>p_i(z)^2=1+p_{i-1}(z)p_{i+1}(z)</math>
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
<h5>history</h5>
 
 
 
* http://www.google.com/search?hl=en&tbs=tl:1&q=
 
 
 
 
 
 
 
 
 
 
 
<h5>related items</h5>
 
 
 
* [[cyclotomic numbers and Chebyshev polynomials]]
 
 
 
 
 
 
 
 
 
 
 
<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103);">encyclopedia</h5>
 
 
 
* http://en.wikipedia.org/wiki/
 
* http://www.scholarpedia.org/
 
* Princeton companion to mathematics([[2910610/attachments/2250873|Companion_to_Mathematics.pdf]])
 
 
 
 
 
 
 
 
 
 
 
<h5>books</h5>
 
 
 
 
 
 
 
* [[2010년 books and articles]]<br>
 
* http://gigapedia.info/1/
 
* http://gigapedia.info/1/
 
* http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
 
 
 
 
 
 
 
 
 
 
 
<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103);">articles</h5>
 
 
 
[[2010년 books and articles|]]
 
 
 
* http://www.ams.org/mathscinet
 
* http://www.zentralblatt-math.org/zmath/en/
 
* http://pythagoras0.springnote.com/
 
* [http://math.berkeley.edu/%7Ereb/papers/index.html 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/
 
 
 
 
 
 
 
 
 
 
 
<h5>question and answers(Math Overflow)</h5>
 
 
 
* http://mathoverflow.net/search?q=
 
* http://mathoverflow.net/search?q=
 
 
 
 
 
 
 
 
 
 
 
<h5>blogs</h5>
 
 
 
*  구글 블로그 검색<br>
 
** http://blogsearch.google.com/blogsearch?q=
 
** http://blogsearch.google.com/blogsearch?q=
 
 
 
 
 
 
 
 
 
 
 
<h5>experts on the field</h5>
 
 
 
* http://arxiv.org/
 
 
 
 
 
 
 
 
 
 
 
<h5>links</h5>
 
 
 
* [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier]
 
* [http://pythagoras0.springnote.com/pages/1947378 수식표 현 안내]
 
* [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences]
 
* http://functions.wolfram.com/
 

2020년 12월 28일 (월) 05:21 기준 최신판