Vector-valued Gelfand-Kazhdan criterion

Fulin Chen; Binyong Sun; Yixiang Weng

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arXiv · 2601.23199

Vector-valued Gelfand-Kazhdan criterion

Fulin Chen·Binyong Sun·Yixiang Weng

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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.

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BibTeX RIS

Fulin Chen, Binyong Sun, Yixiang Weng. 2026-01-30. Vector-valued Gelfand-Kazhdan criterion. https://arxiv.org/abs/2601.23199

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