Geometrization of principal series representations of reductive groups

Kamgarpour, Masoud; Schedler, Travis

doi:10.5802/aif.2988

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Geometrization of principal series representations of reductive groups

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Kamgarpour, Masoud
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.5802/aif.2988
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arXiv:1011.4529.pdf
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Kamgarpour-Schedler_Geometrization of principal series representations of reductive groups_2015.pdf
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Citation

Kamgarpour, M., & Schedler, T. (2015). Geometrization of principal series representations of reductive groups. Annales de l'Institut Fourier, 65(5), 2273-2330. doi:10.5802/aif.2988.

Cite as: https://hdl.handle.net/21.11116/0000-0004-DAE7-2

Abstract

In geometric representation theory, one often wishes to describe representations realized on spaces of invariant functions as trace functions of equivariant perverse sheaves. In the case of principal series representations of a connected split reductive group G over a local field, there is a description of families of these representations realized on spaces of
functions on G invariant under the translation action of the Iwahori subgroup, or a suitable smaller compact open subgroup, studied by Howe, Bushnell and Kutzko, Roche, and others. In this paper, we construct categories of perverse sheaves whose traces recover the families associated to regular characters of T(F_q[[t]]), and prove conjectures of Drinfeld on their structure. We also propose conjectures on the geometrization of families associated to more general characters.