On the degenerate Whittaker space for GL4(o2)

Ankita Parashar; Shiv Prakash Patel

doi:10.1016/j.jpaa.2025.107921

On the degenerate Whittaker space for GL₄(o₂)

Ankita Parashar, Shiv Prakash Patel

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

Abstract

Let o₂ be a finite principal ideal local ring of length 2. For a representation π of GL₄(o₂), the degenerate Whittaker space π_N,ψ is a representation of GL₂(o₂). We describe π_N,ψ explicitly for an irreducible strongly cuspidal representation π of GL₄(o₂). This description verifies a special case of a conjecture of Prasad. We also prove that π_N,ψ is a multiplicity free representation.

Original language	English
Article number	107921
Journal	Journal of Pure and Applied Algebra
Volume	229
Issue number	5
DOIs	https://doi.org/10.1016/j.jpaa.2025.107921
State	Published - 1 May 2025
Externally published	Yes

Keywords

Degenerate Whittaker space
Prasad's conjecture
Regular representations

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1016/j.jpaa.2025.107921

Cite this

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abstract = "Let o2 be a finite principal ideal local ring of length 2. For a representation π of GL4(o2), the degenerate Whittaker space πN,ψ is a representation of GL2(o2). We describe πN,ψ explicitly for an irreducible strongly cuspidal representation π of GL4(o2). This description verifies a special case of a conjecture of Prasad. We also prove that πN,ψ is a multiplicity free representation.",

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KW - Degenerate Whittaker space

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