On degenerate Whittaker space for GL₄(\mathfrako₂)

2024/07/30 by Ankita Parashar, Parashar, Ankita, Shiv Prakash Patel +1
Mathematics · #Advanced Algebra and Geometry #Finite Group Theory Research #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2407.21165

Abstract

Let \mathfrako₂ be a finite principal ideal local ring of length 2. For a representation π of GL₄(\mathfrako₂), the degenerate Whittaker space π_{N, ψ} is a representation of GL₂(\mathfrako₂). We describe π_{N, ψ} explicitly for an irreducible strongly cuspidal representation π of GL₄(\mathfrako₂). This description verifies a special case of a conjecture of Prasad. We also prove that π_{N, ψ} is a multiplicity free representation.

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