Dirac operators on Weil representations I

作者：Pandzic Pavle^*

来源：Mathematical Communications, 2010, 15(2): 401-410.

• symplectic group
• Weil representation
• Dirac operator

Let G be the metaplectic double cover of the group of four-by-four real symplectic matrices. Let g 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 g, and then also with respect to the Kostant's cubic Dirac operator corresponding to a compact Cartan subalgebra of g. The results can be considered as examples illustrating the main results of [11].

• 出版日期2010-12