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Complex algebraic geometry and calculation of multiplicities for induced representations of nilpotent Lie groups

1988
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Transactions of the American Mathematical Society
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Let G be a connected, simply connected nilpotent Lie group, H a Lie subgroup, and a an irreducible unitary representation of H. In a previous paper, the authors and G. Grelaud gave an explicit direct integral decomposition (with multiplicities) of Ind(H î G, a). One consequence of that work was that the multiplicity function was either a.e. infinite or a.e. bounded. In this paper, it is proved that if the multiplicity function is bounded, its parity is a.e. constant. The proof is

doi:10.1090/s0002-9947-1988-0924771-x
fatcat:jz7ussyp5ngjvmsa77ideqmwba