Superbosonisation, Riesz superdistributions, and highest weight modules (extended version)
Alexander Alldridge, Zain Shaikh
TL;DR
This paper explores the mathematical foundations of superbosonisation, connecting it to representation theory and harmonic analysis, and provides new proofs to deepen understanding of its applications in physics.
Contribution
It links superbosonisation to advanced mathematical theories and introduces two novel proofs, enhancing the theoretical framework behind its applications.
Findings
Established connections between superbosonisation and representation theory.
Provided two new proofs of the superbosonisation identity.
Clarified the mathematical underpinnings relevant to physics applications.
Abstract
This is the extended version of a survey prepared for publication in the Springer INdAM series. Superbosonisation, introduced by Littelmann-Sommers-Zirnbauer, is a generalisation of bosonisation, with applications in Random Matrix Theory and Condensed Matter Physics. We link the superbosonisation identity to Representation Theory and Harmonic Analysis and explain two new proofs, one via the Laplace transform and one based on a multiplicity freeness statement.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Random Matrices and Applications · Mathematical Analysis and Transform Methods