The stable wave front set of theta representations

Autor:	Karasiewicz, Edmund, Okada, Emile, Wang, Runze
Rok vydání:	2024
Předmět:	Mathematics - Representation Theory Mathematics - Number Theory 22E50
Druh dokumentu:	Working Paper
Popis:	We compute the stable wave front set of theta representations for certain tame Brylinski-Deligne covers of a connected reductive $p$-adic group. The computation involves two main inputs. First we use a theorem of Okada, adapted to covering groups, to reduce the computation of the wave front set to computing the Kawanaka wave front set of certain representations of finite groups of Lie type. Second, to compute the Kawanaka wave front sets we use Lusztig's formula. This requires a careful analysis of the action of the pro-$p$ Iwahori-Hecke algebra on the theta representation, using the structural results about Hecke algebras developed by Gao-Gurevich-Karasiewicz and Wang. Comment: Main text is 31 pages, followed by 12 pages of tables. 10 tables
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2411.02073 Zobrazit plný text záznamu View this record from Arxiv