29 citations · 89 across the 13 of their papers we have counts for
14 papers
Determinantal representation of colored HOMFLY for double braids
Ya. Kononov, A. Morozov
Starting from the known differential expansions, we express the HOMFLY-PT polynomials of twist and antiparallel double-braid knots in rectangular representations \([r^s]\) as deter…
Cohomology rings of the moduli of one-dimensional sheaves on the projective plane
Yakov Kononov, Woonam Lim, Miguel Moreira +1
We initiate a systematic study on the cohomology rings of the moduli stack of semistable one-dimensional sheaves on the projective plane. We introduce a set of…
Perverse filtrations, Chern filtrations, and refined BPS invariants for local
Yakov Kononov, Weite Pi, Junliang Shen
We explore connections between three structures associated with the cohomology of the moduli of 1-dimensional stable sheaves on : perverse filtrations, tautological c…
Two-dimensional topological theories, rational functions and their tensor envelopes
Mikhail Khovanov, Victor Ostrik, Yakov Kononov
We study generalized Deligne categories and related tensor envelopes for the universal two-dimensional cobordism theories described by rational functions, recently defined by Sazda…
Pursuing quantum difference equations II: 3D-mirror symmetry
Yakov Kononov, Andrey Smirnov
Consider a pair of symplectic varieties dual with respect to 3D-mirror symmetry. The K-theoretic limit of the elliptic duality interface is an equivariant K-theory class of the pro…
Pursuing quantum difference equations I: stable envelopes of subvarieties
Yakov Kononov, Andrey Smirnov
Let be a symplectic variety equipped with an action of a torus . Let be a finite cyclic subgroup. We show that K-theoretic stable envelope of subvarieties $X^ν\…
The 2-leg vertex in K-theoretic DT theory
Ya. Kononov, A. Okounkov, A. Osinenko
K-theoretic Donaldson-Thomas counts of curves in toric and many related threefolds can be computed in terms of a certain canonical 3-valent tensor, the K-theoretic equivariant vert…
On rectangular HOMFLY for twist knots
Ya. Kononov, A. Morozov
As a new step in the study of rectangularly-colored knot polynomials, we reformulate the prescription of arXiv:1606.06015 for twist knots in the double-column representations $R=[r…
Rectangular superpolynomials for the figure-eight knot
Ya. Kononov, A. Morozov
We rewrite the recently proposed differential expansion formula for HOMFLY polynomials of the knot in arbitrary rectangular representation as a sum over all Young s…
On Factorization of Generalized Macdonald Polynomials
Ya. Kononov, A. Morozov
A remarkable feature of Schur functions -- the common eigenfunctions of cut-and-join operators from -- is that they factorize at the peculiar two-parametric topological…
Colored HOMFLY and Generalized Mandelbrot set
Ya. Kononov, A. Morozov
Mandelbrot set is a closure of the set of zeroes of for iterated maps in the moduli space of maps . The wonderful fact is tha…
Flat coordinates for Saito Frobenius manifolds and String theory
Alexander Belavin, Doron Gepner, Yakov Kononov
It was shown in \cite{DVV} for topological Conformal field theory (TCFT) \cite{EY,W} and more recently in \cite{BSZ}-\cite{BB2} for the non-critical String theory \cite{P}-\ci…
Factorization of colored knot polynomials at roots of unity
Ya. Kononov, A. Morozov
From analysis of a big variety of different knots we conclude that at q which is an root of unity, q^{2m}=1, HOMFLY polynomials in symmetric representations [r] satisfy recursion i…
On the defect and stability of differential expansion
Ya. Kononov, A. Morozov
Empirical analysis of many colored knot polynomials, made possible by recent computational advances in Chern-Simons theory, reveals their stability: for any given negative N and an…