Geometry of Kottwitz-Viehmann Varieties
Algebraic Geometry
2018-05-23 v1 Number Theory
Representation Theory
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 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
Cite
@article{arxiv.1805.08770,
title = {Geometry of Kottwitz-Viehmann Varieties},
author = {Jingren Chi},
journal= {arXiv preprint arXiv:1805.08770},
year = {2018}
}
Comments
This article is an expanded and completely rewritten version of arxiv.org/abs/1710.11243. Results have been strengthened and several technical assumptions are removed