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GEOMETRY OF KOTTWITZ–VIEHMANN VARIETIES

Part of: Lie groups Families, fibrations

Published online by Cambridge University Press:  08 November 2019

Jingren Chi Open the ORCID record for Jingren Chi [Opens in a new window]
Jingren Chi*
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742, USA (chijingren@gmail.com)
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Abstract

We study basic geometric properties of Kottwitz–Viehmann varieties, which are certain generalizations of affine Springer fibers that encode orbital integrals of spherical Hecke functions. Based on the previous work of A. Bouthier and the author, we show that these varieties are equidimensional and give a precise formula for their dimension. Also we give a conjectural description of their number of irreducible components in terms of certain weight multiplicities of the Langlands dual group and we prove the conjecture in the case of unramified conjugacy class.

Keywords

affine GrassmannianVinberg monoidspherical Hecke algebraHitchin–Frenkel–Ngô fibration

MSC classification

Primary: 22E35: Analysis on $p$-adic Lie groups 22E67: Loop groups and related constructions, group-theoretic treatment
Secondary: 14D06: Fibrations, degenerations 14D23: Stacks and moduli problems

Information

Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 21 , Issue 1 , January 2022 , pp. 1 - 65
Copyright
© Cambridge University Press 2019

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