Superintegrability summary

Abstract

We enumerate generalizations of the superintegrability property $<character>\sim \mathrm{character}$ and illuminate possible general structures behind them. We collect variations of original formulas available up to date and emphasize the remaining difference between the cases of Hermitian and complex matrices, bosonic and fermionic ones. Especially important is that the story is in no way restricted to Gaussian potentials.

11 pages

References in corpus (3)

• On the complete perturbative solution of one-matrix models
• Correlators in tensor models from character calculus
• Superintegrability of Kontsevich matrix model

Cited by in corpus (33)

• Interpolating Matrix Models for WLZZ series
• Many-body integrable systems implied by WLZZ models
• Superintegrability in $\beta$-deformed Gaussian Hermitian matrix model from $W$-operators
• Commutative subalgebras from Serre relations
• $(q,t)$-deformed (skew) Hurwitz $\tau$-functions
• Hunt for 3-Schur polynomials
• Commutative families in $W_{\infty }$, integrable many-body systems and hypergeometric $\tau$-functions
• On W-operators and superintegrability for dessins d'enfant
• Commutative families in DIM algebra, integrable many-body systems and $q,t$ matrix models
• Spectral curves and $W$-representations of matrix models
• Super-Schur Polynomials for Affine Super Yangian $\mathsf{Y}({\widehat{\mathfrak{gl}}}_{1|1})$
• 3-Schurs from explicit representation of Yangian $Y({\widehat{\mathfrak{gl}}}_1)$. Levels 1-5
• On Chalykh's approach to eigenfunctions of DIM-induced integrable Hamiltonians
• Differential Expansion for antiparallel triple pretzels: the way the factorization is deformed
• Macdonald polynomials for super-partitions
• On character expansion and Gaussian regularization of Itzykson-Zuber measure
• Deformation of superintegrability in the Miwa-deformed Gaussian matrix model
• Towards the theory of Yangians
• Matrix and tensor witnesses of hidden symmetry algebras
• The "Null-A" superintegrability for monomial matrix models
• Defect and degree of the Alexander polynomial
• Row-Column duality and combinatorial topological strings
• Tunnels Under Geometries (or Instantons Know Their Algebras)
• Averaging method in combinatorics of symmetric polynomials
• CMM formula as superintegrability property of unitary model
• Machine learning of the well known things
• Phases in WLZZ Matrix Models
• Towards mixed phase correlators in monomial matrix models
• $\beta$-ensembles and higher genera Catalan numbers
• Equating Schur Functions
• Tau functions of the UC hierarchy as partition functions of matrix models
• Itzykson-Zuber correlators from character expansion
• Quiver Yangian algebras associated to Dynkin diagrams of A-type and their rectangular representations