Class polynomials for some affine Hecke algebras
Zhongwei Yang

TL;DR
This paper computes class polynomials for affine Hecke algebras of type d0A_2 and uses them to prove a conjecture related to affine Deligne-Lusztig varieties for certain groups, revealing interesting patterns.
Contribution
It introduces explicit computations of class polynomials for type d0A_2 affine Hecke algebras and proves a significant conjecture for specific groups using these computations.
Findings
Proved a conjecture of Gf6rtz-Haines-Kottwitz-Reuman for d0GL, unitary, and division algebra groups.
Identified patterns in affine Deligne-Lusztig varieties.
Computed class polynomials explicitly for type d0A_2 affine Hecke algebra.
Abstract
Class polynomials attached to affine Hecke algebras were first introduced by X.~He in \cite{He1}. They play an important role in the study of affine Deligne-Lusztig varieties. Motivated by \cite{He2}, we compute the class polynomials attached to an affine Hecke algebra of type (twisted) . Using these class polynomials we prove a conjecture of G\"{o}rtz-Haines-Kottwitz-Reuman for the general linear group, unitary group and division algebra of semisimple rank 2. Furthermore, we discuss some interesting patterns on affine Deligne-Lusztig varieties.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Mathematical Identities · Advanced Combinatorial Mathematics
