Partial Dirac Cohomology and Tempered Representations

Abstract

The tempered representations of a real reductive Lie group $G$ are naturally partitioned into series associated with conjugacy classes of Cartan subgroups $H$ of $G$. We define partial Dirac cohomology, apply it for geometric construction of various models of these $H$--series representations, and show how this construction fits into the framework of geometric quantization and symplectic reduction.

In this version the Abstract and Introduction were modified for clarity, and one author address was updated. Specifically, the Introduction was split into two parts, labeled Introduction and Statement of Results