Two β-ensemble realization of β-deformed WLZZ models
Abstract
We consider a two β-ensemble realization of the series of β-deformed WLZZ matrix models. We demonstrate that such a realization involves β-deformed Harish-Chandra-Itzykson-Zuber integrals, one of them providing a coupling to the external field. We also construct Ward identities in the corresponding two β-ensemble model, which requires a set of identities for partition function of the one β-ensemble in the external field, and a set of identities for the β-deformed Itzykson-Zuber integral. These both sets of identities are formulated in terms of the Dunkl operators.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.