Lie cohomology of representations of nilpotent Lie groups and holomorphically induced representations
Copyright policy )Lie cohomology of representations of nilpotent Lie groups and holomorphically induced representations
Let U be a locally injective, Moore-Wolf square integrable representa- tion of a nilpotent Lie group N. Let (%, X) be a complex, maximal subordinate pair corresponding to U and let 5Q, = ker X n 3C. The space C°°(U) of differentiable vectors for U is an 3Q module. In this work we compute the Lie algebra cohomology HiCXq, C°°(U)) of this Lie module. We show that the cohomology is zero for all but one value of p and that for this specific value the cohomology is one dimensional. These results, when combined with earlier results of ours, yield the existence and irreducibility of holomorphically induced representations for arbi- trary (nonpositive), totally complex polarizations.
Lie algebra cohomology, Analysis on real and complex Lie groups, differentiable vectors, Nilpotent and solvable Lie groups, holomorphically induced representations, nilpotent Lie group, square integrable representation, Representations of Lie and linear algebraic groups over real fields: analytic methods
Lie algebra cohomology, Analysis on real and complex Lie groups, differentiable vectors, Nilpotent and solvable Lie groups, holomorphically induced representations, nilpotent Lie group, square integrable representation, Representations of Lie and linear algebraic groups over real fields: analytic methods
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