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arXiv · 1609.07456

Bounds on multiplicities of spherical spaces over finite fields

Avraham Aizenbud·Nir Avni
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Abstract

Let $G$ be a reductive group scheme of type $A$ acting on a spherical scheme $X$. We prove that there exists a number $C$ such that the multiplicity $\dim Hom(\rho,\mathbb{C}[X(F)])$ is bounded by $C$, for any finite field $F$ and any irreducible representation $\rho$ of $G(F)$. We give an explicit bound for $C$. We conjecture that this result is true for any reductive group scheme and when $F$ ranges (in addition) over all local fields of characteristic $0$.

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BibTeXRIS

Avraham Aizenbud, Nir Avni. 2016-09-23. Bounds on multiplicities of spherical spaces over finite fields. https://arxiv.org/abs/1609.07456

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