Dirac cohomology and the bottom layer K-types (CROSBI ID 161704)
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Podaci o odgovornosti
Pandžić, Pavle
engleski
Dirac cohomology and the bottom layer K-types
Let $G$ be a connected real reductive Lie group with a maximal compact subgroup $K$ corresponding to a Cartan involution $\Theta$ of $G$. Let $\frqq=\frl\oplus\fru$ be a $\theta$-stable parabolic subalgebra of the complexified Lie algebra $\frg$ of $G$, where $\theta=d\Theta$. Let $L$ be the centralizer of $\frqq$ in $G$. We show that, under certain dominance assumptions, cohomological induction with respect to $\frqq$ takes irreducible unitary $(\frl, L\cap K)$- modules with nonzero Dirac cohomology to irreducible unitary $(\frg, K)$-modules which also have nonzero Dirac cohomology.
real reductive groups; Harish-Chandra modules; Dirac cohomology; cohomological induction; bottom layer K-types
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