Original scientific paper

Dirac operators on Weil representations II

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

Abstract

Let G be a metaplectic double cover of the group G of four-by-four real symplectic matrices.
Let $\frg$ be the complexified Lie algebra of G. Denote by $W_0$ and $W_1$ the Harish-Chandra modules of the even and odd Weil representations of $G$, respectively. We find the Dirac cohomology of $W_0$ and $W_1$ with respect to a noncompact Levi subalgebra $\frl$ of a $\theta$-stable parabolic subalgebra of $\frg$. The
results can be considered as counterexamples to certain generalizations of the main results of [9].

Keywords

symplectic group; Weil representation; Dirac operator

Hrčak ID:

61868

URI

https://hrcak.srce.hr/61868

Publication date:

8.12.2010.

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