The character correspondence in the stable range over a p-adic field
Representation Theory
2023-03-07 v4
Abstract
Given a real irreducible dual pair there is an integral kernel operator which maps the distribution character of an irreducible admissible representation of the group with the smaller or equal rank to an invariant eigendistribution on the group with the larger or equal rank. If the pair is in the stable range and if the representation is unitary, then the resulting distribution is the character of the representation obtained via Howe's correspondence. This construction was transferred to the p-adic case and a conjecture was formulated. In this note we verify a weaker version of this conjecture for dual pairs in the stable range over a p-adic field.
Keywords
Cite
@article{arxiv.2207.07298,
title = {The character correspondence in the stable range over a p-adic field},
author = {Hung Yean Loke and Tomasz Przebinda},
journal= {arXiv preprint arXiv:2207.07298},
year = {2023}
}
Comments
arXiv admin note: text overlap with arXiv:1602.08401