51 citations · 413 across the 41 of their papers we have counts for
40 papers
Miwa deformation of WLZZ matrix models
T. Diudin, A. Popolitov
In this paper we propose a universal way to define multivariate orthogonal polynomials for the positive branch of WLZZ matrix models. This allows us to generalize from the Gaussian…
Non-symmetric triads and Baker-Akhiezer functions
A. Mironov, A. Morozov, A. Popolitov
The symmetric Macdonald polynomial at peculiar values of parameter , is naturally split into non-symmetric parts, which are the (quasi)polynomial…
Cherednik integrable system: eigenfunctions at generic eigenvalues
A. Mironov, A. Morozov, A. Popolitov
Symmetric Macdonald polynomials of variables provide eigenfunctions of the -body trigonometric Ruijsenaars-Schneider integrable system at particular eigenvalues. In order to…
Integrable systems inspired by DAHA and DIM algebra: type versus type
L. Bishler, A. Mironov, A. Popolitov
The Ding-Iohara-Miki (DIM) algebra (quantum toroidal algebra of ) is related to a wide class of quantum many-particle integrable systems, a typical one being the Ru…
Nested ansatz method for Baker-Akhiezer functions
A. Mironov, A. Morozov, A. Popolitov
We explain that the logic behind the derivation of the Noumi-Shiraishi function can be applied directly to the Baker-Akhiezer function (BAF). This amounts to changing an ansatz for…
Twisted Cherednik systems and non-symmetric Macdonald polynomials
A. Mironov, A. Morozov, A. Popolitov
We consider eigenfunctions of many-body system Hamiltonians associated with generalized (a-twisted) Cherednik operators used in construction of other Hamiltonians: those arising fr…
Symmetric polynomials: DIM integrable systems versus twisted Cherednik systems
A. Mironov, A. Morozov, A. Popolitov
We discuss interrelations between eigenfunctions of the Hamiltonians associated with the commutative (integer ray) subalgebras of the Ding-Iohara-Miki algebra and those of the twis…
Twisted Cherednik spectrum as a -deformation
A. Mironov, A. Morozov, A. Popolitov
The common eigenfunctions of the twisted Cherednik operators can be first analyzed in the limit of . Then, the polynomial eigenfunctions form a simple set origi…
Phases in WLZZ Matrix Models
A. Mironov, A. Oreshina, A. Popolitov
We discuss the space of solutions to the Ward identities associated with the WLZZ models. We mostly concentrate on the case of these models described by a two-matrix model with the…
Diamond of triads
A. Mironov, A. Morozov, A. Popolitov +1
The triad refers to embedding of two systems of polynomials, symmetric ones and those of the Baker-Akhiezer type into a power series of the Noumi-Shiraishi type. It provides an alt…
Twisted Baker-Akhiezer function from determinants
A. Mironov, A. Morozov, A. Popolitov
General description of eigenfunctions of integrable Hamiltonians associated with the integer rays of Ding-Iohara-Miki (DIM) algebra, is provided by the theory of Chalykh Baker-Akhi…
Elliptic triad
A. Mironov, A. Morozov, A. Popolitov +1
The triad refers to embedding the Macdonald polynomials into the Noumi-Shiraishi functions and their reduction to solutions of simple linear equations at particular values of .…
CMM formula as superintegrability property of unitary model
A. Mironov, A. Morozov, A. Popolitov
A typical example of superintegrability is provided by expression of the Hopf link hyperpolynomial in an arbitrary representation through a pair of the Macdonald polynomials at spe…
Chalykh's Baker-Akhiezer functions as eigenfunctions of the integer-ray integrable systems
A. Mironov, A. Morozov, A. Popolitov
Macdonald symmetric polynomial at reduces to a sum of much simpler complementary non-symmetric polynomials, which satisfy a simple system of the first order linear diffe…
A basic triad in Macdonald theory
A. Mironov, A. Morozov, A. Popolitov
Within the context of wavefunctions of integrable many-body systems, rational multivariable Baker-Akhiezer (BA) functions were introduced by O. Chalykh, M. Feigin and A. Veselov an…
On Chalykh's approach to eigenfunctions of DIM-induced integrable Hamiltonians
A. Mironov, A. Morozov, A. Popolitov
Quite some years ago, Oleg Chalykh has built a nice theory from the observation that the Macdonald polynomial reduces at to a sum over permutations of simpler polynomial…
Commutative families in DIM algebra, integrable many-body systems and matrix models
A. Mironov, A. Morozov, A. Popolitov
We extend our consideration of commutative subalgebras (rays) in different representations of the algebra to the elliptic Hall algebra (or, equivalently, to the Ding…
-WLZZ models from -ensemble integrals directly
A. Mironov, A. Oreshina, A. Popolitov
Recently, we performed a two -ensemble realization of the series of -deformed WLZZ matrix models involving -deformed Harish-Chandra-Itzykson-Zuber integrals. The realizati…
Deformation of superintegrability in the Miwa-deformed Gaussian matrix model
A. Mironov, A. Morozov, A. Popolitov +1
We consider an arbitrary deformation of the Gaussian matrix model parameterized by Miwa variables . One can look at it as a mixture of the Gaussian and logarithmic (Selberg) p…
Two -ensemble realization of -deformed WLZZ models
A. Mironov, A. Oreshina, A. Popolitov
We consider a two -ensemble realization of the series of -deformed WLZZ matrix models. We demonstrate that such a realization involves -deformed Harish-Chandra-Itzykson-Zu…
Summing up perturbation series around superintegrable point
A. Mironov, A. Morozov, A. Popolitov +1
We work out explicit formulas for correlators in the Gaussian matrix model perturbed by a logarithmic potential, i.e. by inserting Miwa variables. In this paper, we concentrate on…
and algebras, and Ward identities
Ya. Drachov, A. Mironov, A. Popolitov
It was demonstrated recently that the algebra contains commutative subalgebras associated with all integer slope rays (including the vertical one). In this paper, we…
On bilinear superintegrability for monomial matrix models in pure phase
C. -T. Chan, V. Mishnyakov, A. Popolitov +1
We argue that the recently discovered bilinear superintegrability arXiv:2206.02045 generalizes, in a non-trivial way, to monomial matrix models in pure phase. The structure is much…
Commutative subalgebras from Serre relations
A. Mironov, V. Mishnyakov, A. Morozov +1
We demonstrate that commutativity of numerous one-dimensional subalgebras in algebra, i.e. the existence of many non-trivial integrable systems described in recent a…