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arXiv · 1211.6199

The Projective Envelope of a Cuspidal Representation of a Finite Linear Group

David Paige
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Abstract

Let $\ell$ be a prime and let $q$ be a prime power not divisible by $\ell$. Put $G=\mathrm{GL}_n(\mathrm{F}_q)$ and fix an irreducible cuspidal representation, $\barπ$, of $G$ over a sufficiently large finite field, $k$, of characteristic $\ell$ such that $\barπ$ is not supercuspidal. We compute the $\mathrm{W}(k)[G]$-endomorphism ring of the projective envelope of $\barπ$ under the assumption that $\ell>n$. Our computations provide evidence for a conjecture of Helm relating the Bernstein center to the deformation theory of Galois representations.

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David Paige. 2012-11-27. The Projective Envelope of a Cuspidal Representation of a Finite Linear Group. https://arxiv.org/abs/1211.6199

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