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

1979 ◽  
Vol 242 (2) ◽  
pp. 103-126 ◽  
Author(s):  
Henryk Hecht
Keyword(s):  
Lie Group ◽  
Reductive Lie Group

scholarly journals Mellin Transforms of Whittaker Functions

2002 ◽  
Vol 45 (3) ◽  
pp. 364-377
Author(s):  
Anton Deitmar
Keyword(s):  
Lie Group ◽  
Meromorphic Functions ◽  
Whittaker Functions ◽  
Mellin Transforms ◽  
Reductive Lie Group

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.

Parabolic Higgs Bundles for Real Reductive Lie Groups

2018 ◽  
pp. 653-680 ◽  
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.

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

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

scholarly journals Convexity theorems for the gradient map on probability measures

2018 ◽  
Vol 5 (1) ◽  
pp. 133-145 ◽  
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.

scholarly journals Wave front sets of reductive Lie group representations

2016 ◽  
Author(s):  
Benjamin Harris ◽  
Hongyu He ◽  
Gestur Ólafsson
Keyword(s):  
Wave Front ◽  
Lie Group ◽  
Group Representations ◽  
Wave Front Sets ◽  
Reductive Lie Group

scholarly journals Wave front sets of reductive Lie group representations III

2017 ◽  
Vol 313 ◽  
pp. 176-236 ◽  
Author(s):  
Benjamin Harris ◽  
Tobias Weich
Keyword(s):  
Wave Front ◽  
Lie Group ◽  
Group Representations ◽  
Wave Front Sets ◽  
Reductive Lie Group

On the Analytic Continuation of c-Functions

1988 ◽  
Vol 40 (3) ◽  
pp. 513-531
Author(s):  
Paul F. Ringseth
Keyword(s):  
Analytic Continuation ◽  
Eisenstein Series ◽  
Lie Group ◽  
Spectral Decomposition ◽  
The Subject ◽  
Reductive Lie Group ◽  
Difficult Part

Let G be a reductive Lie group; Γ a nonuniform lattice in G. Then the theory of Eisenstein series plays a major role in the spectral decomposition of L2(G/Γ) (cf. [5]). One of the most difficult aspects of the subject is the analytic continuation of the Eisenstein series along with its associated c-function. This was originally done by Langlands using some very difficult analysis (cf. [5]). Later Harish-Chandra was able to simplify somewhat the most difficult part of the continuation, the continuation to zero, by the introduction of the Maas-Selberg relation. The purpose of this note is to give a simplified account of this particular part of the theory.Our chief tool will be the truncation operator of Arthur (cf. [1] and [8]), the systematic utilization of which has the effect of streamlining the earlier accounts, especially in so far as continuation to zero is concerned, which is reduced to an elementary manipulation.

scholarly journals THE CONTINUOUS SPECTRUM IN DISCRETE SERIES BRANCHING LAWS

2013 ◽  
Vol 24 (07) ◽  
pp. 1350049 ◽  
Author(s):  
BENJAMIN HARRIS ◽  
HONGYU HE ◽  
GESTUR ÓLAFSSON
Keyword(s):  
Continuous Spectrum ◽  
Lie Group ◽  
Discrete Series ◽  
Series Representation ◽  
Direct Integral ◽  
Branching Laws ◽  
Reductive Lie Group ◽  
A New Technique ◽  
Direct Integral Decomposition ◽  
Integral Decomposition

If G is a reductive Lie group of Harish-Chandra class, H is a symmetric subgroup, and π is a discrete series representation of G, the authors give a condition on the pair (G, H) which guarantees that the direct integral decomposition of π|H contains each irreducible representation of H with finite multiplicity. In addition, if G is a reductive Lie group of Harish-Chandra class, and H ⊂ G is a closed, reductive subgroup of Harish-Chandra class, the authors show that the multiplicity function in the direct integral decomposition of π|H is constant along "continuous parameters". In obtaining these results, the authors develop a new technique for studying multiplicities in the restriction π|H via convolution with Harish-Chandra characters. This technique has the advantage of being useful for studying the continuous spectrum as well as the discrete spectrum.

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