17 citations · 44 across the 6 of their papers we have counts for
6 papers
Categorification of the genus two DAHA
Semeon Arthamonov, Ievgen Makedonskyi, Daniil Sarafannikov
We construct three derived endofunctors on the derived category of graded integrable representations of the current algebra of a flat degeneration of , and prove that the…
Quasi-Poisson varieties from double quasi-Poisson algebras in types
Semeon Arthamonov, Maxime Fairon
Double (quasi-)Poisson brackets were introduced on associative algebras by Van den Bergh to induce a (quasi-)Poisson structure on their representation spaces naturally equipped wit…
Cluster structure on genus 2 spherical DAHA: seven-colored flower
Semeon Arthamonov, Leonid Chekhov, Philippe Di Francesco +4
We construct an embedding of the Arthamonov-Shakirov algebra of genus 2 knot operators into the quantized coordinate ring of the cluster Poisson variety of exceptional finite mutat…
Superintegrable Systems on Moduli Spaces of Flat Connections
S. Arthamonov, N. Reshetikhin
The main result of this paper is the construction of a family of superintegrable Hamiltonian systems on moduli spaces of flat connections on a principle -bundle on a surface. Th…
Modified Double Poisson Brackets
Semeon Arthamonov
We propose a non skew-symmetric generalization of the original definition of double Poisson Bracket by M. Van den Bergh. It allows one to explicitly construct more general class of…
Noncommutative Inverse Scattering Method for the Kontsevich system
Semeon Arthamonov
We formulate an analog of Inverse Scattering Method for integrable systems on noncommutative associative algebras. In particular we define Hamilton flows, Casimir elements and nonc…