Jingren Chi
Published 2018-05-22Version 1
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.
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
On the fundamental domain of affine Springer fibers
Dimensions of Affine Springer Fibers for Some $\mathrm{GL}_n$ Symmetric Spaces
On the local behavior of weighted orbital integrals and the affine Springer fibers
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