On epsilon factors attached to supercuspidal representations of unramified \(\mathrm{U}(2,1)\) (Q2838127)
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scientific article; zbMATH DE number 6185208
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On epsilon factors attached to supercuspidal representations of unramified \(\mathrm{U}(2,1)\) |
scientific article; zbMATH DE number 6185208 |
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8 July 2013
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\(p\)-adic groups
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local new forms
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\(\epsilon\)-factors
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On epsilon factors attached to supercuspidal representations of unramified \(\mathrm{U}(2,1)\) (English)
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Let \(G\) be the unramified unitary group of three variables defined over a \(p\)-adic field \(F\) with \(p \neq 2\). Then generic irreducible representations of \(G\) determine zeta integrals of Rankin-Selberg type, which were studied by Gelbart, Piatetski-Shapiro and Baruch.NEWLINENEWLINEIn this paper, the author introduces a conjecture describing \(L\)-factors and \(\epsilon\)-factors defined by such zeta integrals in terms of new forms for \(G\), which is similar to a result obtained by Casselman and Deligne for \(p\)-adic new forms for \(GL (2)\). He then proves this conjecture for generic supercuspidal representations of \(G\).
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