Naslov
Dirac operators on Weil representations I

Autori
Pandžić, Pavle

Izvornik
Mathematical communications (1331-0623) 15 (2010), 2; 401-410

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

Ključne riječi
Symplectic group; Weil representation; Dirac operator; Dirac cohomology

Sažetak
Let $G$ be the metaplectic double cover of the group of four-by-four real symplectic matrices. Let $\frg$ be the complexified Lie algebra of $G$. Let $W_0$ and $W_1$ be the Harish-Chandra modules of the even respectively odd Weil representations of $G$. We find the Dirac cohomology of $W_0$ and $W_1$ with respect to the Dirac operator corresponding to a maximal compact subalgebra of $\frg$, and then also with respect to the Kostant's cubic Dirac operator corresponding to a compact Cartan subalgebra of $\frg$. The results can be considered as examples illustrating the main results of \cite{; ; HPR}; ; .

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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