Forum of Mathematics, Sigma (May 2014)

SUPERBOSONIZATION VIA RIESZ SUPERDISTRIBUTIONS

  • ALEXANDER ALLDRIDGE,
  • ZAIN SHAIKH

DOI
https://doi.org/10.1017/fms.2014.5
Journal volume & issue
Vol. 2

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.

Keywords