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- W1978444701 abstract "Let G be either the metaplectic double cover of Sp(2n, ℝ), or SO*(2n), or SU(p, q). Let g be the complexified Lie algebra of G and let K be a maximal compact subgroup of G. Let X be one of the Wallach modules for the pair (g, K). In other words, X corresponds to a discrete point in the classification of unitary lowest weight modules with scalar lowest K-type. The purpose of this paper is to calculate the Dirac cohomology of X. Our approach is based on the explicit knowledge of the K-types of X. We establish a bijection between certain K-types E i of X and certain K-types F i of the spin module, where K is the spin double cover of K. The Dirac cohomology is then realized as the set of Parthasarathy-Ranga-Rao-Varadarajan components of E i ⊗ F i ." @default.
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- W1978444701 date "2011-03-01" @default.
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- W1978444701 title "Dirac cohomology of Wallach representations" @default.
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- W1978444701 doi "https://doi.org/10.2140/pjm.2011.250.163" @default.
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