On Residues of Intertwining Operators in Cases with Prehomogeneous Nilradical

Autor:	Sandeep Varma
Rok vydání:	2017
Předmět:	Pure mathematics Transfer (group theory) Induced representation Distribution (number theory) Group (mathematics) General Mathematics Irreducibility Abelian group Reductive group Levi decomposition Mathematics
Zdroj:	Canadian Journal of Mathematics. 69:1169-1200
ISSN:	1496-4279 0008-414X
Popis:	Let P = M N be a Levi decomposition of a maximal parabolic subgroup of a connected reductive group G over a p-adic field F. Assume that there exists w0∊ G(F) that normalizes M and conjugates P to an opposite parabolic subgroup. When N has a Zariski dense Int M-orbit, F. Shahidi and X. Yu described a certain distribution D on M(F), such that, for irreducible unitary supercuspidal representations π of M(F) withis irreducible if and only if D( f )≠ 0 for some pseudocoefficient f of π. Since this irreducibility is conjecturally related to π arising via transfer from certain twisted endoscopic groups of M, it is of interest to realize D as endoscopic transfer from a simpler distribution on a twisted endoscopic group H of M. This has been done in many situations where N is abelian. Here we handle the standard examples in cases where N is nonabelian but admit a Zariski dense Int M-orbit.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::229ddbd851b3a6909226c85b2bc961df https://doi.org/10.4153/cjm-2016-032-3 Zobrazit plný text záznamu