Lie Algebra Cohomology and Holomorphic Continuation of Generalized Jacquet Integrals

Nolan R. Wallach

Type: Article

Publication Date: 2018-06-06

Citations: 22

DOI: https://doi.org/10.2969/aspm/01410123

Abstract

We now describe the other type of results.Let lJ be the sum of the eigenspaces for ad H with non-negative eigenvalue.Let P = {g e G \ Ad(g)lJClJ} and put M=Pn0(P).Let (a, H,) be a finite dimensional irreducible representation of M. Put a={Z em I [Z, m]=O, 0Z= -Z}.If v e at then let (rrP,,,., l"l,,,) be the corresponding (degenerate) principal series representation (see § 6).Let r=exp (rr/2(x-Y)).The analytic results involve the study of integrals of the form JP,,,,(f) = L eiB(Y,ulf.,h•exp (u))du.

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