Smooth Fréchet globalizations of Harish-Chandra modules

Bernstein, Joseph; Krötz, Bernhard

doi:10.1007/s11856-013-0056-1

Cited by 92 publications

(131 citation statements)

References 12 publications

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“…On the other hand, consider an irreducible smooth complex representation (π, V π ) of G(F ) in a suitable category. When F = R, the natural choice are the SAF representations (smooth admissible Fréchet of moderate growth), also known as Casselman-Wallach representations; see [4]. Denote the continuous Hom space N π := Hom G (π, C ∞ (X + )).…”

Section: Introductionmentioning

confidence: 99%

Towards Generalized Prehomogeneous Zeta Integrals

2018

Lecture Notes in Mathematics

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Let X be a prehomogeneous vector space under a connected reductive group G over R.Assume that the open G-orbit X + admits a finite covering by a symmetric space. We study certain zeta integrals involving (i) Schwartz functions on X, and (ii) generalized matrix coefficients on X + (R) of Casselman-Wallach representations of G(R), upon a twist by complex powers of relative invariants. This merges representation theory with prehomogeneous zeta integrals of Igusa et al. We show their convergence in some shifted cone, and prove their meromorphic continuation via the machinery of bfunction together with V. Ginzburg's results on admissible D-modules. This provides some evidence for a broader theory of zeta integrals associated to affine spherical embeddings.

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Section: Introductionmentioning

confidence: 99%

Towards Generalized Prehomogeneous Zeta Integrals

2018

Lecture Notes in Mathematics

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“…11.6.7 or [2]) this embedding extends to a continuous embedding of Fréchet spaces V ∞ → E ∞ w . In particular, there exists a continuous norm q on V ∞ such that…”

Section: Symmetric Spacesmentioning

confidence: 90%

“…Thus the smooth vectors E ∞ w form an S F-representation of G in the sense of [2] (that is a smooth Fréchet representation of moderate growth).…”

Section: Symmetric Spacesmentioning

confidence: 99%

Decay of matrix coefficients on reductive homogeneous spaces of spherical type

2014

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“…Remark 5.13. An equivalent way to phrase the globalization theorem is as follows (see [4]). Let V = τ ∈ K V [τ ] be the K-isotypical decomposition of V .…”

Section: This Brings Us Finally To Thementioning

confidence: 99%