Gelfand criterion and multiplicity one results for GL n over finite chain rings

Shiv Prakash Patel; Pooja Singla

doi:10.1007/s13226-021-00188-4

Gelfand criterion and multiplicity one results for GL _n over finite chain rings

Shiv Prakash Patel, Pooja Singla

Research output: Contribution to journal › Article › peer-review

Abstract

We study the Whittaker space of GL _n(O/ (ϖ^ℓ)) where ℓ≥ 1 , O is the ring of integers of a non-Archimedean local field and ϖ is a uniformizer of O. By using Gelfand criterion, we prove that the Whittaker space is multiplicity free for n= 2 , 3. We also state a few related open questions.

Original language	English
Pages (from-to)	761-772
Number of pages	12
Journal	Indian Journal of Pure and Applied Mathematics
Volume	52
Issue number	3
DOIs	https://doi.org/10.1007/s13226-021-00188-4
State	Published - 1 Sep 2021
Externally published	Yes

Keywords

Gelfand criterion
Gelfand–Graev model
Multiplicity one
Whittaker space

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1007/s13226-021-00188-4

Cite this

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abstract = "We study the Whittaker space of GL n(O/ (ϖℓ)) where ℓ≥ 1 , O is the ring of integers of a non-Archimedean local field and ϖ is a uniformizer of O. By using Gelfand criterion, we prove that the Whittaker space is multiplicity free for n= 2 , 3. We also state a few related open questions.",

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