Naslov
Dirac operators and unitarizability of Harish- Chandra modules

Autori
Pandžić, Pavle

Izvornik
Mathematical communications (1331-0623) 15 (2010), 1; 273-279

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Dirac operator; unitary representation; Harish-Chandra module

Sažetak
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 $M\otimes S$.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA