arXiv Analytics

Sign in

arXiv:1804.05043 [math.RT]AbstractReferencesReviewsResources

Representations of reductive groups over finite local rings of length two

Alexander Stasinski, Andrea Vera-Gajardo

Published 2018-04-13Version 1

Let $\mathbb{F}_{q}$ be a finite field of characteristic $p$, and let $W_{2}(\mathbb{F}_{q})$ be the ring of Witt vectors of length two over $\mathbb{F}_{q}$. We prove that for any reductive group scheme $\mathbb{G}$ over $\mathbb{Z}$ such that $p$ is very good for $\mathbb{G}\times\mathbb{F}_{q}$, the groups $\mathbb{G}(\mathbb{F}_{q}[t]/t^{2})$ and $\mathbb{G}(W_{2}(\mathbb{F}_{q}))$ have the same number of irreducible representations of dimension $d$, for each $d$. Equivalently, there exists an isomorphism of group algebras $\mathbb{C}[\mathbb{G}(\mathbb{F}_{q}[t]/t^{2})]\cong\mathbb{C}[\mathbb{G}(W_{2}(\mathbb{F}_{q}))]$.

Related articles: Most relevant | Search more
arXiv:1609.07456 [math.RT] (Published 2016-09-23)
Bounds on multiplicities of spherical spaces over finite fields
arXiv:1612.01109 [math.RT] (Published 2016-12-04)
The Ismagilov conjecture over a finite field ${\mathbb F}_p$
arXiv:1310.1596 [math.RT] (Published 2013-10-06)
On multiplication of double cosets for $\GL(\infty)$ over a finite field