Original scientific paper

Dirac operators on Weil representations I

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

Abstract

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 and odd Weil representations of G, respectively.
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 [11].

Keywords

symplectic group; Weil representation; Dirac operator

Hrčak ID:

61867

URI

https://hrcak.srce.hr/61867

Publication date:

8.12.2010.

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