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# On cuspidal representations of general linear groups over discrete valuation rings

Aubert, Anne-Marie, Onn, Uri, Prasad, Amritanshu and Stasinski, Alexander (2009) On cuspidal representations of general linear groups over discrete valuation rings. Israel Journal of Mathematics, 21pp. (Submitted)

Record type: Article

## Abstract

We define a new notion of cuspidality for representations of $\GL_n$ over a finite quotient $\Oh_k$ of the ring of integers $\Oh$ of a non-Archimedean local field $F$ using geometric and infinitesimal induction functors, which involve automorphism groups $G_\lambda$ of torsion $\Oh$\nobreakdash-modules. When $n$ is a prime, we show that this notion of cuspidality is equivalent to strong cuspidality, which arises in the construction of supercuspidal representations of $\GL_n(F)$. We show that strongly cuspidal representations share many features of cuspidal representations of finite general linear groups. In the function field case, we show that the construction of the representations of $\GL_n(\Oh_k)$ for $k\geq 2$ for all $n$ is equivalent to the construction of the representations of all the groups $G_\lambda$. A functional equation for zeta functions for representations of $\GL_n(\Oh_k)$ is established for representations which are not contained in an infinitesimally induced representation. All the cuspidal representations for $\GL_4(\Oh_2)$ are constructed. Not all these representations are strongly cuspidal

Full text not available from this repository.

Submitted date: 2009

## Identifiers

Local EPrints ID: 69674
URI: http://eprints.soton.ac.uk/id/eprint/69674
ISSN: 0021-2172
PURE UUID: 36bd9513-4b9e-48a7-a2c9-706cbb84d303

## Catalogue record

Date deposited: 27 Nov 2009

## Contributors

Author: Anne-Marie Aubert
Author: Uri Onn
Author: Alexander Stasinski

## University divisions

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