"Finite dimensional representations of Sl(2)"의 두 판 사이의 차이
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| 1번째 줄: | 1번째 줄: | ||
<h5>introduction</h5> | <h5>introduction</h5> | ||
| − | + | * http://qchu.wordpress.com/2010/03/07/walks-on-graphs-and-tensor-products/ | |
| 7번째 줄: | 7번째 줄: | ||
| − | <h5>character formula</h5> | + | <h5>character formula of sl(2)</h5> |
* Weyl-Kac formula<br><math>ch(V)={\sum_{w\in W} (-1)^{\ell(w)}w(e^{\lambda+\rho}) \over e^{\rho}\prod_{\alpha>0}(1-e^{-\alpha})}</math><br> | * Weyl-Kac formula<br><math>ch(V)={\sum_{w\in W} (-1)^{\ell(w)}w(e^{\lambda+\rho}) \over e^{\rho}\prod_{\alpha>0}(1-e^{-\alpha})}</math><br> | ||
| 20번째 줄: | 20번째 줄: | ||
* <math>U_{n+1}(x) & = 2xU_n(x) - U_{n-1}(x)</math> | * <math>U_{n+1}(x) & = 2xU_n(x) - U_{n-1}(x)</math> | ||
| − | |||
| 82번째 줄: | 81번째 줄: | ||
[[2010년 books and articles|]] | [[2010년 books and articles|]] | ||
| + | * [http://dx.doi.org/10.1063/1.527759 SL(2,C), SU(2), and Chebyshev polynomials]<br> | ||
| + | ** Henri Bacry, J. Math. Phys. 28, 2259 (1987) | ||
* http://www.ams.org/mathscinet | * http://www.ams.org/mathscinet | ||
* http://www.zentralblatt-math.org/zmath/en/ | * http://www.zentralblatt-math.org/zmath/en/ | ||
| 88번째 줄: | 89번째 줄: | ||
* http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q= | * 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://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/ | + | * http://dx.doi.org/10.1063/1.527759 |
2010년 4월 4일 (일) 19:39 판
introduction
character formula of sl(2)
- Weyl-Kac formula
\(ch(V)={\sum_{w\in W} (-1)^{\ell(w)}w(e^{\lambda+\rho}) \over e^{\rho}\prod_{\alpha>0}(1-e^{-\alpha})}\)
- for trivial representation, we get denominator identity
\({\sum_{w\in W} (-1)^{\ell(w)}w(e^{\rho}) = e^{\rho}\prod_{\alpha>0}(1-e^{-\alpha})^{m_{\alpha}}}\)
Chebyshev polynomial
- \(U_{n+1}(x) & = 2xU_n(x) - U_{n-1}(x)\)
\(p_i(z)=\frac{w^{i+1}-w^{-i-1}}{w-w^{-1}}\) for \( i=1,\cdots, k\)
- \(p_{0}(z)=1\)
- \(p_{1}(z)=z\)
- \(p_i(z)^2=1+p_{i-1}(z)p_{i+1}(z)\)
history
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|]]
- SL(2,C), SU(2), and Chebyshev polynomials
- Henri Bacry, J. Math. Phys. 28, 2259 (1987)
- 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/10.1063/1.527759
question and answers(Math Overflow)
blogs
experts on the field