We realize the fundamental representations of quantum algebras via the supersymmetric
Higgs mechanism in gauge theories with 8 supercharges on an $\Omega $-background. We …

We consider 5d supersymmetric gauge theories with unitary groups in the Ω-background
and study codim-2/4 BPS defects supported on orthogonal planes intersecting at the origin …

A bstract Quantum curves arise from Seiberg-Witten curves associated to 4d\(\mathcal {N}\)=
2 gauge theories by promoting coordinates to non-commutative operators. In this way the …

A detailed review of the p, q-duality for Calogero system and its generalizations is given. For
the first time, we present some of elliptic-trigonometric Hamiltonians dual to the elliptic …

We demonstrate that the symmetric elliptic polynomials\(E_\lambda (x)\) originally
discovered in the study of generalized Noumi–Shiraishi functions are eigenfunctions of the …

A bstract In this study we map the dualities observed in the framework of integrable
probabilities into the dualities familiar in a realm of integrable many-body systems. The …

The Inozemtsev chain is an exactly solvable interpolation between the short-range
Heisenberg and long-range Haldane–Shastry (HS) chains. In order to unlock its potential to …

A bstract As a development of [1], we note that the ordinary Shiraishi functions have an
insufficient number of parameters to describe generic eigenfunctions of double elliptic …

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 …

This paper is intended to serve as a review of a series of papers with Nikita Nekrasov, where
we achieved several important results concerning the relation between the moduli space of …