Partially harmonic spinors and representations of reductive Lie groups |
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Authors: | Joseph A Wolf |
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Institution: | Department of Mathematics, University of California, Berkeley, California 94720 U.S.A. |
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Abstract: | Let G be a reductive Lie group subject to some minor technical restrictions. The Plancherel Theorem for G uses several series of unitary representation classes, one series for each conjugacy class of Cartan subgroups of G. Given a Cartan subgroup H ? G, we construct a G-homogeneous family X → Y of oriented riemannian symmetric spaces, some G-homogeneous bundles , and some Hilbert spaces of partially harmonic spinors with values in . Then G acts on by a unitary representation πμ,σ±. We then show that these πμ,σ± realize the series of representation classes of G associated to the conjugacy class of H. |
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