Gelfand--Graev representation as a Hecke algebra module of simple types of a finite central cover of $\mathrm{GL}(r)$
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917918606884864 |
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| author | Zou, Jiandi |
| author_facet | Zou, Jiandi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07262 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gelfand--Graev representation as a Hecke algebra module of simple types of a finite central cover of $\mathrm{GL}(r)$ Zou, Jiandi Representation Theory Number Theory 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. |
| title | Gelfand--Graev representation as a Hecke algebra module of simple types of a finite central cover of $\mathrm{GL}(r)$ |
| topic | Representation Theory Number Theory |
| url | https://arxiv.org/abs/2502.07262 |