Original scientific paper

https://doi.org/10.3336/gm.45.2.12

Dirac cohomology and the bottom layer K-types

Pavle Pandžić orcid.org/0000-0002-7405-4381 ; Department of Mathematics, University of Zagreb, Bijenička 30, 10 000 Zagreb, Croatia

Abstract

Let G be a connected real reductive Lie group with a maximal compact subgroup K corresponding to a Cartan involution Θ of G. Let q=l u be a θ-stable parabolic subalgebra of the complexified Lie algebra g of G, where θ=dΘ. Let L be the centralizer of q in G. We show that, under certain dominance assumptions, cohomological induction with respect to q takes irreducible unitary (l, L ∩ K)-modules with nonzero Dirac cohomology to irreducible unitary (g,K)-modules which also have nonzero Dirac cohomology.

Keywords

Reductive Lie group; unitary representation; Harish-Chandra module; Dirac operator; Dirac cohomology; cohomological induction; bottom layer

Hrčak ID:

62700

URI

https://hrcak.srce.hr/62700

Publication date:

24.12.2010.

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