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Journal of the Institute of Mathematics of Jussieu (1)

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1 results

GEOMETRY OF KOTTWITZ–VIEHMANN VARIETIES
Part of
- Families, fibrations
- Lie groups
Jingren Chi
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 21 / Issue 1 / January 2022

Published online by Cambridge University Press:

08 November 2019, pp. 1-65

Print publication:

January 2022
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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.