349 citations · 600 across the 36 of their papers we have counts for
38 papers
Regular pullback of generalized cluster structures
Misha Gekhtman, Michael Shapiro, Alek Vainshtein
We consider the problem of lifting a regular cluster structure on a quasi-affine variety to the ambient affine space and a similar problem of defining a regular pullback of a regul…
A generalized cluster structure on via birational Poisson maps
Misha Gekhtman, Michael Shapiro, Alek Vainshtein
In a recent work, we constructed a rational map from a simple Lie group to itself that intertwines the standard Poisson--Lie structure on with a Poisson h…
A unified approach to exotic cluster structures on simple Lie groups
Misha Gekhtman, Michael Shapiro, Alek Vainshtein
We propose a new approach to building log-canonical coordinate charts for any simply-connected simple Lie group $\G$ and arbitrary Poisson-homogeneous bracket on $\G$ associated wi…
Generalized Cluster Structures Related to the Drinfeld Double of
Misha Gekhtman, Michael Shapiro, Alek Vainshtein
We prove that the regular generalized cluster structure on the Drinfeld double of constructed in arXiv:1912.00453 is complete and compatible with the standard Poisson--Lie s…
Periodic staircase matrices and generalized cluster structures
Misha Gekhtman, Michael Shapiro, Alek Vainshtein
As is well-known, cluster transformations in cluster structures of geometric type are often modeled on determinant identities, such as short Plucker relations, Desnanot--Jacobi ide…
Plethora of cluster structures on
Misha Gekhtman, Michael Shapiro, Alek Vainshtein
We continue the study of multiple cluster structures in the rings of regular functions on , and that are compatible with Poisson-Lie and Poisson…