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edited Nov 10, 2011 at 23:22

Jon Bannon

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Informations What information is contained in the Kazhdan Lusztig-Lusztig polynomials?

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asked Nov 10, 2011 at 20:57

Jan Weidner

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Informations contained in Kazhdan Lusztig polynomials

The Kazhdan-Lusztig polynomials contain all kinds of representation theoretic (and other kinds of) informations.

For example the character of a simple module over a Lie algebra with Weyl group $W$ can be read of from the KL-polynomials in the following way: $$ch(L_w)=\sum_y (-1)^{l(w)-l(y)}P_{y,w}(1) ch(M_y)$$ here $L_w$ resp. $M_w$ denote the simple resp. Verma module of highest weight $-w(\rho) -\rho$.

What are other examples of important information encoded in KL-Polynomials?