Towards elliptic deformation of $q,t$-matrix models

Abstract

As a necessary step in constructing elliptic matrix models, which preserve the superintegrability property $<char>\sim \mathrm{char}$, we suggest an elliptic deformation of the peculiar loci $p_k^{{\Delta }_n}$, which play an important role in precise formulation of this property. The suggestion is to define the $p_k^{{\Delta }_n}$-loci as elliptic functions with the right asymptotics at $\tau \to i\infty$. If this hypothesis is correct, one can move to substituting the Schur and Macdonald functions in the role of characters by the elliptic GNS and study their behavior at the deformed topological and $\Delta$ loci.

arXiv comment5 pages

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Cited by in corpus (6)

• Superintegrability in $\beta$-deformed Gaussian Hermitian matrix model from $W$-operators
• Commutative families in DIM algebra, integrable many-body systems and $q,t$ matrix models
• Bilinear character correlators in superintegrable theory
• Elliptic $q,t$ matrix models
• Deformation of superintegrability in the Miwa-deformed Gaussian matrix model
• CMM formula as superintegrability property of unitary model