60 citations · 203 across the 21 of their papers we have counts for
21 papers
Hecke and Artin monoids and their homomorphisms
Arkady Berenstein, Jacob Greenstein, Jian-Rong Li
The aim of the present work is to systematically study homomorphisms of Hecke and Artin monoids and thus to develop their comprehensive theory. Our original motivation was the stri…
On cacti and crystals
Arkady Berenstein, Jacob Greenstein, Jian-Rong Li
In the present work we study actions of various groups generated by involutions on the category of integrable highest weight -mo…
Canonical bases of quantum Schubert cells and their symmetries
Arkady Berenstein, Jacob Greenstein
The goal of this work is to provide an elementary construction of the canonical basis in each quantum Schubert cell~ and to establish its invariance under mo…
Koszul duality for semidirect products and generalized Takiff algebras
Jacob Greenstein, Volodymyr Mazorchuk
We obtain Koszul-type dualities for categories of graded modules over a graded associative algebra which can be realized as the semidirect product of a bialgebra coinciding with it…
Generalized Joseph's decompositions
Arkady Berenstein, Jacob Greenstein
We generalize the decomposition of introduced by A. Joseph and relate it, for semisimple, to the celebrated computation of central elements due to…
Integrable clusters
Arkady Berenstein, Jacob Greenstein, David Kazhdan
The goal of this note is to study quantum clusters in which cluster variables (not coefficients) commute which each other. It turns out that this property is preserved by mutations…