Restriction to compact subgroups in the cyclic homology of reductive p-adic groups

TL;DR

This paper investigates how restriction operators to compact subgroups interact with various representation-theoretic operators in the cyclic homology of Hecke algebras of reductive p-adic groups.

Contribution

It analyzes the commutation relations between restriction operators and key operators like Jacquet functors, Bernstein centre idempotents, and characters in the context of cyclic homology.

Findings

Restriction operators commute with Jacquet functors under certain conditions

Identification of non-commuting cases with explicit examples

Enhanced understanding of the structure of cyclic homology in p-adic groups

Abstract

Restriction of functions from a reductive p-adic group G to its compact subgroups defines an operator on the Hochschild and cyclic homology of the Hecke algebra of G. We study the commutation relations between this operator and others coming from representation theory: Jacquet functors, idempotents in the Bernstein centre, and characters of admissible representations.