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math.RT2026
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…
math.RT2026
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…
math.RT2024
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…