A $(-q)$-analogue of weight multiplicities

Details A $(-q)$-analogue of weight multiplicities A $(-q)$-analogue of weight multiplicities

2012-03-02

arxiv.org/abs/1203.0521v1

Mathematics

Representation Theory

21 pages

Scientific paper

We prove a conjecture in \cite{L} stating that certain polynomials $P^{\sigma}_{y,w}(q)$ introduced in \cite{LV1} for twisted involutions in an affine Weyl group give $(-q)$-analogues of weight multiplicities of the Langlands dual group $\check{G}$. We also prove that the signature of a naturally defined hermitian form on each irreducible representation of $\check{G}$ can be expressed in terms of these polynomials $P^{\sigma}_{y,w}(q)$.

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