157 citations · 380 across the 12 of their papers we have counts for
12 papers
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…
A note on universality in refined Chern-Simons theory
Andrei Mironov, Ruben Mkrtchyan
We discuss various forms of refinements of Vogel's universality in Chern-Simons theory. While the original universality applies to arbitrary simple Lie groups, its counterpart in r…
Macdonald deformation of Vogel's universality and link hyperpolynomials
Liudmila Bishler, Andrei Mironov, Alexei Morozov
Vogel's universality implies a unified description of the adjoint sector of representation theory for simple Lie algebras in terms of three parameters , which are homogeneou…
Torus knots in adjoint representation and Vogel's universality
Liudmila Bishler, Andrei Mironov
Vogel's universality gives a unified description of the adjoint sector of representation theory for simple Lie algebras in terms of three parameters , which are homogeneous…
On Refined Vogel's universality
Liudmila Bishler, Andrei Mironov
In accordance with P. Vogel, a set of algebra structures in Chern-Simons theory can be made universal, independent of a particular family of simple Lie algebras. In particular, thi…
Tensorial generalization of characters
H. Itoyama, A. Mironov, A. Morozov
In rainbow tensor models, which generalize rectangular complex matrix model (RCM) and possess a huge gauge symmetry , we introduce a new sub-basis…
A non-torus link from topological vertex
H. Awata, H. Kanno, A. Mironov +2
The recently suggested tangle calculus for knot polynomials is intimately related to topological string considerations and can help to build the HOMFLY-PT invariants from the topol…
Orthogonal Polynomials in Mathematical Physics
Chuan-Tsung Chan, A. Mironov, A. Morozov +1
This is a review of (-)hypergeometric orthogonal polynomials and their relation to representation theory of quantum groups, to matrix models, to integrable theory, and to knot t…
Universal Racah matrices and adjoint knot polynomials. I. Arborescent knots
A. Mironov, A. Morozov
By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of s…
SU(2)/SL(2) knot invariants and KS monodromies
D. Galakhov, A. Mironov, A. Morozov
We review the Reshetikhin-Turaev approach to construction of non-compact knot invariants involving R-matrices associated with infinite-dimensional representations, primarily those…
Algebra of differential operators associated with Young diagrams
A. Mironov, A. Morozov, S. Natanzon
We establish a correspondence between Young diagrams and differential operators of infinitely many variables. These operators form a commutative associative algebra isomorphic to t…
Complete Set of Cut-and-Join Operators in Hurwitz-Kontsevich Theory
A. Mironov, A. Morozov, S. Natanzon
We define cut-and-join operator in Hurwitz theory for merging of two branching points of arbitrary type. These operators have two alternative descriptions:(i) they have the GL char…