The irreducible unitary $\mathrm {GL} (n-1,\mathbb {R})$-spherical representations of $\mathrm {SL} (n, \mathbb {R})$

G. Van Dijk; M. Poel

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A duality in the theory of group representations

A. Wawrzyńczyk (1970)

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Spherical unitary dual of general linear group over non-Archimidean local field

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Let $F$ be a local non-archimedean field. The set of all equivalence classes of irreducible spherical representations of $G L (n, F)$ is described in the first part of the paper. In particular, it is shown that each irreducible spherical representation is parabolically induced by an unramified character. Bernstein’s result on the irreducibility of the parabolically induced representations of $G L (n, F)$ by irreducible unitary ones, and Ol’shanskij’s construction of complementary series give directly a description...

The Plancherel formula for the pseudo-riemannian space $SL (n, ℝ) / GL (n - 1, ℝ)$

G. Van Dijk, M. Poel (1986)

Compositio Mathematica

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On some series of representations related to symmetric spaces

H. Schlichtkrull (1984)

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Paul J.jun. Sally, Marko Tadic (1993)

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On Kirillov's conjecture for archimedean fields

Siddhartha Sahi (1989)

Compositio Mathematica

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Displaying similar documents to “The irreducible unitary GL ( n - 1 , ℝ ) -spherical representations of SL ( n , ℝ ) ”

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On Kirillov's conjecture for archimedean fields

Displaying similar documents to “The irreducible unitary $GL (n - 1, ℝ)$ -spherical representations of $SL (n, ℝ)$ ”

The Plancherel formula for the pseudo-riemannian space $SL (n, ℝ) / GL (n - 1, ℝ)$

Induced representations and classification for $G S p (2, F)$ and $S p (2, F)$

Representations of $p$ -adic symplectic groups