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- Title
Virasoro Versus Superintegrability. Gaussian Hermitian Model.
- Authors
Mironov, A.; Mishnyakov, V.; Morozov, A.; Rashkov, R.
- Abstract
Relation between the Virasoro constraints and KP integrability (determinant formulas) for matrix models is a lasting mystery. We elaborate on the claim that the situation is improved when integrability is enhanced to superintegrability, i.e., to explicit formulas for Gaussian averages of characters. In this case, the Virasoro constraints are equivalent to simple recursive formulas, which have appropriate combinations of characters as their solutions. Moreover, one can easily separate dependence on the size of matrix, and deduce superintegrability from the Virasoro constraints. We describe one of the ways to do so for the Gaussian Hermitian matrix model. The result is a spectacularly elegant reformulation of Virasoro constraints as identities for the Schur functions evaluated at appropriate loci in the space of time-variables.
- Subjects
SCHUR functions
- Publication
JETP Letters, 2021, Vol 113, Issue 11, p728
- ISSN
0021-3640
- Publication type
Article
- DOI
10.1134/S0021364021120018