Dmitriy Voloshyn

collaborators

3 papers

math.RT2025

Multiple rational normal forms in Lie theory

Dmitriy Voloshyn

We study the decomposition of a generic element $g \in G$ of a connected reductive complex algebraic group $G$ in the form $g = N (g) B (g) u ˉ N (g)^{- 1}$ where $N: G \dashrighta…

math.QA2025

Generalized cluster structures related to Poisson duals of $SL_{n}$

Michael Gekhtman, Dmitriy Voloshyn

We study Poisson varieties $(SL_{n}, I ¨ _{I^ ˉ}^{†})$ parameterized by Belavin--Drinfeld quadruples $I^ ˉ := (I^, r_{0})$ of type $A_{n - 1}$ along…

math.RT2025

Starfish lemma via birational quasi-isomorphisms

Dmitriy Voloshyn

We study birational quasi-isomorphisms between normal Noetherian domains endowed with cluster structures of geometric type. We prove an analogue of the Starfish lemma that allows o…

Multiple rational normal forms in Lie theory

Generalized cluster structures related to Poisson duals of SLn​

Starfish lemma via birational quasi-isomorphisms

Generalized cluster structures related to Poisson duals of $SL_{n}$