Vector-valued Gelfand-Kazhdan criterion
Representation Theory
2026-02-02 v1
Abstract
The Gelfand-Kazhdan criterion is a fundamental tool for studying multiplicity-one properties of local periods of representations. However, it does not apply to many cases arising in the relative Langlands program. Generalizing the usual Gelfand-Kazhdan criterion, we formulate and prove a vector-valued Gelfand-Kazhdan criterion that fits into the general framework of the relative Langlands program. As an illustration of its effectiveness, we establish the multiplicity-one property for the local Asai Rankin-Selberg periods.
Cite
@article{arxiv.2601.23199,
title = {Vector-valued Gelfand-Kazhdan criterion},
author = {Fulin Chen and Binyong Sun and Yixiang Weng},
journal= {arXiv preprint arXiv:2601.23199},
year = {2026}
}