engleski

Classification of Aq(λ) modules by their Dirac cohomology for type D, G2 and sp(2n, R)

Abstract. Let G be a connected real reductive group with maximal compact subgroup K of the same rank as G. In the recent paper of Huang, Pandžić and Vogan, it was shown that the admissible Θ–stable parabolic subalgebras q of g are in one-to-one correspodence with the faces of W ρ intersecting the k–dominant Weyl chamber and that A q (0)–modules can be classified by their Dirac cohomology in geometric terms. They described in detail the cases when g 0 is of type A, B, F and C except for g 0 = sp(2n, R). We will describe faces corresponding to A q (0)–modules for g 0 = sp(2n, R) and for g 0 of type D and G 2

(g, K)-module ; A q (λ) module ; Dirac cohomology

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