Mellin Transforms of Whittaker Functions

AbstractIn this note we show that for an arbitrary reductive Lie group and any admissible irreducible Banach representation the Mellin transforms of Whittaker functions extend to meromorphic functions. We locate the possible poles and show that they always lie along translates of walls of Weyl chambers.

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On characters and asymptotics of representations of a real reductive Lie group

Mathematische Annalen ◽

10.1007/bf01420410 ◽

1979 ◽

Vol 242 (2) ◽

pp. 103-126 ◽

Cited By ~ 7

Author(s):

Henryk Hecht

Keyword(s):

Lie Group ◽

Reductive Lie Group

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Parabolic Higgs Bundles for Real Reductive Lie Groups

Geometry and Physics: Volume II ◽

10.1093/oso/9780198802020.003.0027 ◽

2018 ◽

pp. 653-680 ◽

Cited By ~ 1

Author(s):

Ignasi Mundet i Riera

Keyword(s):

Riemann Surface ◽

Lie Groups ◽

Lie Group ◽

Vector Bundles ◽

Structure Group ◽

Higgs Bundles ◽

Local Systems ◽

Parabolic Structure ◽

Reductive Lie Groups ◽

Reductive Lie Group

This chapter explains the correspondence between local systems on a punctured Riemann surface with the structure group being a real reductive Lie group G, and parabolic G-Higgs bundles. The chapter describes the objects involved in this correspondence, taking some time to motivate them by recalling the definitions of G-Higgs bundles without parabolic structure and of parabolic vector bundles. Finally, it explains the relevant polystability condition and the correspondence between local systems and Higgs bundles.

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A theorem on the Schwartz space of a reductive Lie group

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.72.12.4718 ◽

1975 ◽

Vol 72 (12) ◽

pp. 4718-4719 ◽

Cited By ~ 7

Author(s):

J. Arthur

Keyword(s):

Lie Group ◽

Schwartz Space ◽

Reductive Lie Group

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A comparison of Paley–Wiener theorems for real reductive Lie groups

Journal für die reine und angewandte Mathematik (Crelles Journal) ◽

10.1515/crelle-2012-0105 ◽

2014 ◽

Vol 2014 (695) ◽

Author(s):

Erik P. van den Ban ◽

Sofiane Souaifi

Keyword(s):

Lie Groups ◽

Lie Group ◽

Detailed Comparison ◽

Reductive Lie Groups ◽

Reductive Lie Group

AbstractIn this paper we make a detailed comparison between the Paley–Wiener theorems of J. Arthur and P. Delorme for a real reductive Lie group

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Convexity theorems for the gradient map on probability measures

Complex Manifolds ◽

10.1515/coma-2018-0008 ◽

2018 ◽

Vol 5 (1) ◽

pp. 133-145 ◽

Cited By ~ 2

Author(s):

Leonardo Biliotti ◽

Alberto Raffero

Keyword(s):

Lie Group ◽

Kähler Manifold ◽

Probability Measures ◽

Kahler Manifold ◽

Abelian Case ◽

Real Submanifold ◽

Reductive Lie Group

AbstractGiven a Kähler manifold (Z, J, ω) and a compact real submanifold M ⊂ Z, we study the properties of the gradient map associated with the action of a noncompact real reductive Lie group G on the space of probability measures on M. In particular, we prove convexity results for such map when G is Abelian and we investigate how to extend them to the non-Abelian case.

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