engleski

Dirac cohomology of Wallach representations

We compute the Dirac cohomology of the unitary Harish-Chandra modules for classical groups lifted from 1- dimensional representations of the compact factors in Howe duality, including all Wallach modules. Our approach is based on the explicit knowledge of the $K$-types of these Harish-Chandra modules and of the spinor module for the maximal compact subgroup. Our description of the Dirac cohomology is an explicit pairing between these $K$-types in terms of their PRV components.

Harish-Chandra module; Dirac cohomology; Wallach representation

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