On the decomposition of a representation of \(GL(3)\) restricted to \(GL(2)\) over a \(p\)-adic field

DOI10.1215/S0012-7094-93-06908-6zbMath0827.22006OpenAlexW1511916494MaRDI QIDQ1210440

Dipendra Prasad

Publication date: 8 August 1993

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-93-06908-6

zbMATH Keywords

restrictioninduced representationsWhittaker modelsirreducible admissible representationsWeil group representationsnonarchimedean local field

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Induced representations for locally compact groups (22D30)

Related Items (12)

Restriction for general linear groups: the local non-tempered Gan-Gross-Prasad conjecture (non-Archimedean case) ⋮ A vanishing Ext-branching theorem for \((\mathrm{GL}_{n+1}(F),\mathrm{GL}_n(F)\) ⋮ Square integrability of representations on \(p\)-adic symmetric spaces ⋮ Unnamed Item ⋮ Multiplicity one theorems ⋮ Shintani functions and automorphic \(L\)-functions for \(GL(n)\) ⋮ Ext-multiplicity theorem for standard representations of \((\mathrm{GL}_{n+1},\mathrm{GL}_n)\) ⋮ On representations of \(\mathrm{GL}(n)\) distinguished by \(\mathrm{GL}(n - 1)\) over a \(p\)-adic field ⋮ Linear and Shalika local periods for the mirabolic group, and some consequences ⋮ Relative discrete series representations for two quotients of $p$-adic $\mathbf{GL}_n$ ⋮ Homological branching law for \((\mathrm{GL}_{n+1}(F), \mathrm{GL}_n(F))\): projectivity and indecomposability ⋮ The non-tempered \(\theta_{10}\) Arthur parameter and Gross-Prasad conjectures

Cites Work

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• Admissible representations of a semi-simple group over a local field with vectors fixed under an Iwahori subgroup
• Automorphic forms on \(GL(3)\). I, II
• Rankin-Selberg Convolutions
• Induced representations of reductive ${\germ p}$-adic groups. I

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