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Dirac operators and unitarizability of Harish- Chandra modules (CROSBI ID 156220)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Pandžić, Pavle Dirac operators and unitarizability of Harish- Chandra modules // Mathematical communications, 15 (2010), 1; 273-279

Podaci o odgovornosti

Pandžić, Pavle

engleski

Dirac operators and unitarizability of Harish- Chandra modules

Let $G$ be a simple noncompact Lie group. Let $K$ be a maximal compact subgroup of $G$, and let $\frg=\frk\oplus\frp$ be the corresponding Cartan decomposition of the complexified Lie algebra $\frg$ of $G$. We give a criterion for a $(\frg, K)$-module $M$ to be unitary in terms of the action of the Dirac operator $D$ on $M\otimes S$, where $S$ is a spin module for $C(\frp)$. More precisely, we show that an arbitrary Hermitian inner product on $M$ will be invariant if and only if $D$ is symmetric with respect to the corresponding inner product on $M\otimes S$.

Dirac operator; unitary representation; Harish-Chandra module

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Podaci o izdanju

15 (1)

2010.

273-279

objavljeno

1331-0623

Povezanost rada

Matematika

Indeksiranost