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

Abstract

We prove a conjecture in \cite{L} stating that certain polynomials $P_{y,w}^{\sigma }(q)$ 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 $P_{y,w}^{\sigma }(q)$.

21 pages

Cited by in corpus (1)

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