Generalized Whittaker functions for degenerate principal series of \(\mathrm{GL}(n, \mathbb{R})\)

DOI10.2977/PRIMS/88zbMath1259.22011OpenAlexW2145975885MaRDI QIDQ1932212

Kazuki Hiroe

Publication date: 17 January 2013

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/88

zbMATH Keywords

hypergeometric functionsgeneral linear groupdegenerate principal seriesmultiplicity one theoremsgeneralized Whittaker model

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Cites Work

• Generalized Jacquet modules of parabolically induced representations
• Asymptotic behavior of matrix coefficients of admissible representations
• Whittaker functions on semisimple Lie groups
• Whittaker vectors and the Goodman-Wallach operators
• Hecke-Siegel's pull-back formula for the Epstein zeta function with a harmonic polynomial
• On the functional equations satisfied by Eisenstein series
• Eigenfunctions of invariant differential operators on a symmetric space
• Whittaker functions for \(P_J\)-principal series representations of \(\text{Sp}(3,\mathbb R)\)
• A duality for symmetric spaces with applications to group representations
• A quantization of conjugacy classes of matrices
• The Chowla-Selberg Method for Fourier Expansion of Higher Rank Eisenstein Series
• Theory of prehomogeneous vector spaces (algebraic part)—the English translation of Sato’s lecture from Shintani’s note
• UNITARY REPRESENTATIONS OF NILPOTENT LIE GROUPS
• On the Horn system of partial differential equations and series of hypergeometric type
• Bessel Series Expansions of the Epstein Zeta Function and the Functional Equation
• Holomorphic continuation of generalized Jacquet integrals for degenerate principal series
• Automorphic Forms and L-Functions for the GroupGL(n, R)
• On Whittaker vectors for generalized Gelfand-Graev representations of semisimple Lie groups
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