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SUPERBOSONIZATION VIA RIESZ SUPERDISTRIBUTIONS

Part of: Calculus on manifolds; nonlinear operators Lie groups Other (nonclassical) types of functional analysis

Published online by Cambridge University Press:  14 May 2014

ALEXANDER ALLDRIDGE Open the ORCID record for ALEXANDER ALLDRIDGE [Opens in a new window]  and
ZAIN SHAIKH
ALEXANDER ALLDRIDGE
Affiliation:
Universität zu Köln, Mathematisches Institut, Weyertal 86-90, 50931 Köln, Germany; alldridg@math.uni-koeln.de
ZAIN SHAIKH
Affiliation:
Universität Paderborn, Institut für Mathematik, Fakultät EIM, Warburger Str. 100, 33100 Paderborn, Germany

Abstract

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The superbosonization identity of Littelmann, Sommers and Zirnbauer is a new tool for use in studying universality of random matrix ensembles via supersymmetry, which is applicable to non-Gaussian invariant distributions. We give a new conceptual interpretation of this formula, linking it to harmonic superanalysis of Lie supergroups and symmetric superspaces, and in particular, to a supergeneralization of the Riesz distributions. Using the super-Laplace transformation of generalized superfunctions, the theory of which we develop, we reduce the proof to computing the Gindikin gamma function of a Riemannian symmetric superspace, which we determine explicitly.

MSC classification

Secondary: 22E30: Analysis on real and complex Lie groups 58C50: Analysis on supermanifolds or graded manifolds 22E45: Representations of Lie and linear algebraic groups over real fields 46S60: Functional analysis on superspaces (supermanifolds) or graded spaces
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 2 , 01 July 2014 , e9
Creative Commons
Creative Common License - CCCreative Common License - BY
The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution licence .
Copyright
© The Author(s) 2014

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