Gelfand--Graev representation as a Hecke algebra module of simple types of a finite central cover of $\mathrm{GL}(r)$

Jiandi Zou

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arXiv · 2502.07262

Gelfand--Graev representation as a Hecke algebra module of simple types of a finite central cover of $\mathrm{GL}(r)$

Jiandi Zou

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Abstract

For an $n$-fold Kazhdan--Patterson cover or Savin's cover of a general linear group over a non-archimedean local field of residual characteristic $p$ with $\mathrm{gcd}(n,p)=1$, we realize the Gelfand--Graev representation as a Hecke algebra module of a simple type and study its explicit expression. As a main corollary, we calculate the Whittaker dimension of every discrete series representation of such a cover. Using Zelevinsky's classification, this theoretically gives the Whittaker dimension of every irreducible representation.

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Jiandi Zou. 2025-02-11. Gelfand--Graev representation as a Hecke algebra module of simple types of a finite central cover of $\mathrm{GL}(r)$. https://arxiv.org/abs/2502.07262

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