We construct the (β-deformed) partition function hierarchies with W-representations. Based
on the W-representations, we analyze the superintegrability property and derive their …

We suggest a two-matrix model depending on three (infinite) sets of parameters which
interpolates between all the models proposed in Wang et al.(Eur Phys JC 82: 902, arXiv …

In the case of SU (2), associated by the AGT relation to the 2d Liouville theory, the Seiberg-
Witten prepotential is constructed from the Bohr-Sommerfeld periods of 1d sine-Gordon …

We enumerate generalizations of the superintegrability property< character>∼ character
and illuminate possible general structures behind them. We collect variations of original …

We provide some details about the recently discovered integrable systems implied by
commutativity of W operators along the rays on the plane of roots of w∞-algebra. The …

Since the (β-deformed) hermitian one-matrix models can be represented as the integrated
conformal field theory (CFT) expectation values, we construct the operators in terms of the …

Ward identities in the most general “network matrix model” from [1] can be described in
terms of the Ding–Iohara–Miki algebras (DIM). This confirms an expectation that such …

We follow the general recipe for constructing commutative families of W-operators, which
provides Hurwitz-like expansions in symmetric functions (Macdonald polynomials), in order …

A bstract There is now a renewed interest [1]–[4] to a Hurwitz τ-function, counting the
isomorphism classes of Belyi pairs, arising in the study of equilateral triangulations and …

We give a concise summary of the impressive recent development unifying a number of
different fundamental subjects. The quiver Nekrasov functions (generalized hypergeometric …