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arXiv · 1203.0521

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

George Lusztig·Zhiwei Yun
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Abstract

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

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George Lusztig, Zhiwei Yun. 2012-03-02. A $(-q)$-analogue of weight multiplicities. https://arxiv.org/abs/1203.0521

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