Harmonic Analysis on Reductive Groups pp 209-222 | Cite as

# Intertwining Functors and Irreducibility of Standard Harish—Chandra Sheaves

## Abstract

Let g be a complex semisimple Lie algebra and *σ* an involution of g. Denote by t the fixed point set of this involution. Let *K* be a connected algebraic group and ϕ a morphism of *K* into the group *G* = Int(**g**) of inner automorphisms of g such that its differential is injective and identifies the Lie algebra of *K* with t. Let *X* be the flag variety of g, i.e. the variety of all Borel subalgebras in g. Then *K* acts algebraically on *X*, and it has finitely many orbits which are locally closed smooth sub varieties. The typical situation is the following: g is the complexification of the Lie algebra of a connected real semisimple Lie group *G* _{0} with finite center, *K* is the complexification of a maximal compact subgroup of *G* _{0}, and *σ* the corresponding Cartan involution.

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