Geometrization of principal series representations of reductive groups

Kamgarpour, Masoud and Schedler, Travis (2015) Geometrization of principal series representations of reductive groups. Annales de l'Institut Fourier, 65 5: 2273-2330. doi:10.5802/aif.2988

Author Kamgarpour, Masoud
Schedler, Travis
Title Geometrization of principal series representations of reductive groups
Journal name Annales de l'Institut Fourier   Check publisher's open access policy
ISSN 0373-0956
Publication date 2015-01-01
Sub-type Article (original research)
DOI 10.5802/aif.2988
Open Access Status DOI
Volume 65
Issue 5
Start page 2273
End page 2330
Total pages 58
Place of publication Saint-Martin-d'Heres, France
Publisher Association des Annales de l'Institut Fourier
Language eng
Formatted 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(Fq[[t]]), and prove conjectures of Drinfeld on their structure. We also propose conjectures on the geometrization of families associated to more general characters.
Keyword Clean perverse sheaves
Compact open subgroups
Geometric Satake isomorphism
Hecke algebras
Principal series representations
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2016 Collection
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