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Restriction of holomorphic discrete series to real forms / Jorge Antonio Vargas.

By: Vargas, Jorge Antonio, 1949-.
Material type: materialTypeLabelBookSeries: Trabajos de Matemática. Serie A / Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física ; no. 60.Publisher: Córdoba, Argentina : Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física, 2000Description: 9 p. ; 30 cm.Subject(s): Semisimple Lie groups and their representations | Lie Groups | Grupos de Lie | Grupos de Lie | Discrete series representationsOnline resources: Versión Digital Summary: Let G be a connected linear semisimple Lie group having a Holomorphic Discrete Series representation π. Let H be a connected semisimple group of G so that the global symmetric space attached to H is a real form of the Hermitian symmetric space associated to G. Fix a maxial compact subgroup K of G so that H ∩ K is a maximal compact subgroup for H. Let τ be the lowest K_type for a π and let τ* denote the restriction of τ to H ∩ K. In this note we prove that the restriction of π to H is unitarily equivalent to the unitary representation of H induced by τ* .
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Let G be a connected linear semisimple Lie group having a Holomorphic Discrete Series representation π. Let H be a connected semisimple group of G so that the global symmetric space attached to H is a real form of the Hermitian symmetric space associated to G. Fix a maxial compact subgroup K of G so that H ∩ K is a maximal compact subgroup for H. Let τ be the lowest K_type for a π and let τ* denote the restriction of τ to H ∩ K. In this note we prove that the restriction of π to H is unitarily equivalent to the unitary representation of H induced by τ* .

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