Gamma sheaves on reductive groups

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The purpose of this paper is to introduce and study certain irreducible perverse l-adic sheaves on a reductive group G over a finite field (we call them gamma-sheaves). One can construct such a sheaf starting with (almost) every finite-dimensional representation of the Langlands dual group. We present conjecture connecting the above sheaves with generalized gamma-functions introduced in our previous paper. We also conjecture that the convolution functor with the above sheaves enjoys certain nice properties (in particular, we compute the convolution of a gamma-sheaf with a character sheaf). We prove the above conjectures for G of semi-simple rank 0 or 1 and (partially) for G=GL(n).
to appear in Schur memorial volume

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Algebraic Geometry, Representation Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/62148

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0109033
 http://arxiv.org/abs/math/0109033

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arXiv