17 citations · 131 across the 20 of their papers we have counts for
20 papers
Super-Hamiltonians for super-Macdonald polynomials
Dmitry Galakhov, Alexei Morozov, Nikita Tselousov
The Macdonald finite-difference Hamiltonian is lifted to a super-generalization. In addition to canonical bosonic time variables new Grassmann time variables are introd…
Macdonald polynomials for super-partitions
Dmitry Galakhov, Alexei Morozov, Nikita Tselousov
We introduce generalization of famous Macdonald polynomials for the case of super-Young diagrams that contain half-boxes on the equal footing with full boxes. These super-Macdonald…
Supersymmetric polynomials and algebro-combinatorial duality
Dmitry Galakhov, Alexei Morozov, Nikita Tselousov
In this note we develop a systematic combinatorial definition for constructed earlier supersymmetric polynomial families. These polynomial families generalize canonical Schur, Jack…
Algorithms for representations of quiver Yangian algebras
Dmitry Galakhov, Alexei Gavshin, Alexei Morozov +1
In this note, we aim to review algorithms for constructing crystal representations of quiver Yangians in detail. Quiver Yangians are believed to describe an action of the BPS algeb…
Wall-Crossing Effects on Quiver BPS Algebras
Dmitry Galakhov, Alexei Morozov, Nikita Tselousov
BPS states in supersymmetric theories can admit additional algebro-geometric structures in their spectra, described as quiver Yangian algebras. Equivariant fixed points on the quiv…
Simple Representations of BPS Algebras: the case of
Dmitry Galakhov, Alexei Morozov, Nikita Tselousov
BPS algebras are the symmetries of a wide class of brane-inspired models. They are closely related to Yangians -- the peculiar and somewhat sophisticated limit of DIM algebras. Sti…
Towards the theory of Yangians
Dmitry Galakhov, Alexei Morozov, Nikita Tselousov
We review the main ideas underlying the emerging theory of Yangians -- the new type of hidden symmetry in string-inspired models. Their classification by quivers is a far-going gen…
Super-Schur Polynomials for Affine Super Yangian
Dmitry Galakhov, Alexei Morozov, Nikita Tselousov
We explicitly construct cut-and-join operators and their eigenfunctions -- the Super-Schur functions -- for the case of the affine super-Yangian $\mathsf{Y}(\widehat{\mathfrak{gl}}…
3-Schurs from explicit representation of Yangian . Levels 1-5
A. Morozov, N. Tselousov
We suggest an ansatz for representation of affine Yangian by differential operators in the triangular set of time-variables with $1\leqs…
Hunt for 3-Schur polynomials
A. Morozov, N. Tselousov
This paper describes our attempt to understand the recent success of Na Wang in constructing the 3-Schur polynomials, associated with the plane partitions. We provide a rather deta…
On an alternative stratification of knots
E. Lanina, A. Popolitov, N. Tselousov
We introduce an alternative stratification of knots: by the size of lattice on which a knot can be first met. Using this classification, we find ratio of unknots and knots with mor…
Differential Expansion for antiparallel triple pretzels: the way the factorization is deformed
A. Morozov, N. Tselousov
For a peculiar family of double braid knots there is a remarkable factorization formula for the coefficients of the differential (cyclotomic) expansion (DE), which nowadays is wide…
Evolution properties of the knot's defect
A. Morozov, N. Tselousov
The defect of differential (cyclotomic) expansion for colored HOMFLY-PT polynomials is conjectured to be invariant under any antiparallel evolution and change linearly with the evo…
Polynomial representations of classical Lie algebras and flag varieties
A. Morozov, M. Reva, N. Tselousov +1
Recently we have started a program to describe the action of Lie algebras associated with Dynkin-type diagrams on generic Verma modules in terms of polynomial vector fields. In thi…
Implications for colored HOMFLY polynomials from explicit formulas for group-theoretical structure
E. Lanina, A. Sleptsov, N. Tselousov
We have recently proposed arXiv:2105.11565 a powerful method for computing group factors of the perturbative series expansion of the Wilson loop in the Chern-Simons theory with $SU…
Irreducible representations of simple Lie algebras by differential operators
A. Morozov, M. Reva, N. Tselousov +1
We describe a systematic method to construct arbitrary highest-weight modules, including arbitrary finite-dimensional representations, for any finite dimensional simple Lie algebra…
Chern-Simons perturbative series revisited
E. Lanina, A. Sleptsov, N. Tselousov
A group-theoretical structure in a perturbative expansion of the Wilson loops in the 3d Chern-Simons theory with gauge group is studied in symmetric approach. A special bas…
Are Maxwell knots integrable?
A. Morozov, N. Tselousov
We review properties of the null-field solutions of source-free Maxwell equations. We focus on the electric and magnetic field lines, especially on limit cycles, which actually can…
A novel symmetry of colored HOMFLY polynomials coming from superalgebras
V. Mishnyakov, A. Sleptsov, N. Tselousov
We present a novel symmetry of the colored HOMFLY polynomial. It relates pairs of polynomials colored by different representations at specific values of and generalizes the pre…
A new symmetry of the colored Alexander polynomial
V. Mishnyakov, A. Sleptsov, N. Tselousov
We present a new conjectural symmetry of the colored Alexander polynomial, that is the specialization of the quantum invariant widely known as the colored HOMFLY-…