Irreducibility criteria for local and global representations

DOI10.1090/S0002-9939-2012-11438-8zbMath1294.11074arXiv1105.5169OpenAlexW2066061559MaRDI QIDQ4911544

Ralf Schmidt, Hiro-aki Narita, Ameya Pitale

Publication date: 19 March 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.5169

zbMATH Keywords

automorphic representationHecke eigenvectorirreducibility of representationsrepresentation over local fields

Mathematics Subject Classification ID

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Related Items (8)

Non-vanishing and sign changes of Hecke eigenvalues for Siegel cusp forms of genus two. With an appendix by E. Kowalski and A. Saha. ⋮ On the theta correspondence for (𝐺𝑆𝑝(4),𝐺𝑆𝑂(4,2)) and Shalika periods ⋮ On special Bessel periods and the Gross-Prasad conjecture for \(\mathrm {SO}(2n+1) \times \mathrm {SO}(2)\) ⋮ Explicit refinements of Böcherer's conjecture for Siegel modular forms of squarefree level ⋮ An explicit lifting construction of CAP forms on O(1,5) ⋮ An explicit construction of non-tempered cusp forms on \(\mathrm{O}(1,8n+1)\) ⋮ Transfer of Siegel cusp forms of degree 2 ⋮ A relation between multiplicity one and Böcherer's conjecture

Cites Work

• The theory of Jacobi forms
• Iwahori-spherical representations of \(\mathrm{GSp}(4)\) and Siegel modular forms of degree 2 with square-free level
• Automorphic Forms on Adele Groups. (AM-83)
• Elements of the representation theory of the Jacobi group
• Siegel modular forms, \(L\)-functions, and Satake parameters
• Siegel modular forms and representations
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