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The centralizer of K in U(g) otimes C(p) for the group SOe(4, 1)

Let G be the Lie group SOe(4, 1), with maximal compact subgroup K = S(O(4) × O(1))e≅ SO(4). Let g =50(5, ℂ) be the complexification of the Lie algebra g0 = 50(4, 1) of G, and let U(g) be the universal enveloping algebra of gk0. Let g = k  p be the Cartan decomposition of 𝔤, and C(𝔭) the Clifford algebra of 𝔭 with respect to the trace form B(X, Y) = tr(XY) on 𝔭. In this paper we give explicit generators of the algebra (U(𝔤) ⊗ C(𝔭)^K.

Lie group ; Lie algebra ; representation ; Dirac operator ; Dirac cohomology

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