Whittaker vectors and the Goodman-Wallach operators

DOI10.1007/BF02392298zbMath0723.22019MaRDI QIDQ757621

Hisayosi Matumoto

Publication date: 1988

Published in: Acta Mathematica (Search for Journal in Brave)

zbMATH Keywords

highest weightIwasawa decompositioncomplexified Lie algebraconnected real semisimple Lie groupglobal Whittaker vectorsirreducible Harish-Chandra module

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Universal enveloping (super)algebras (17B35) Analysis on real and complex Lie groups (22E30) Semisimple Lie groups and their representations (22E46) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

Related Items (17)

Whittaker functions for \(P_J\)-principal series representations of \(\text{Sp}(3,\mathbb R)\) ⋮ Representation theory of \(\mathcal{W}\)-algebras ⋮ Contravariant pairings between standard Whittaker modules and Verma modules ⋮ Archimedean zeta integrals for 𝐺𝐿(3)×𝐺𝐿(2) ⋮ Generalized Whittaker functions for degenerate principal series of \(\mathrm{GL}(n, \mathbb{R})\) ⋮ Principal series and generalized principal series Whittaker functions with peripheral \(K\)-types on the real symplectic group of rank 2 ⋮ Annihilator varieties, adduced representations, Whittaker functionals, and rank for unitary representations of \(GL(n)\) ⋮ Kostant's problem for Whittaker modules ⋮ Unnamed Item ⋮ Whittaker functions for generalized principal series representations of \(\mathrm{SL}(3, \mathbb R)\) ⋮ Unnamed Item ⋮ $C^{-\infty}$-Whittaker vectors for complex semisimple Lie groups, wave front sets, and Goldie rank polynomial representations ⋮ Whittaker modules associated with highest weight modules ⋮ Deficient homomorphisms between generalized Verma modules ⋮ On the composition series of the standard Whittaker $(\mathfrak {g},K)$-modules ⋮ Socle filtrations of the standard Whittaker \((\mathfrak{g},K)\)-modules of Spin\((r,1)\) ⋮ Secondary Whittaker functions for \(P_J\)-principal series representations of \(\text{Sp}(3,\mathbb R)\)

Cites Work

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