7 citations · 12 across the 3 of their papers we have counts for
6 papers
Noncommutative Double Bruhat cells and their factorizations
Arkady Berenstein, Vladimir Retakh
In the present paper we study noncommutative double Bruhat cells. Our main results are explicit positive matrix factorizations in the cells via quasiminors of matrices with noncomm…
Quantum cluster algebras
Arkady Berenstein, Andrei Zelevinsky
Cluster algebras were introduced by S. Fomin and A. Zelevinsky in math.RT/0104151; their study continued in math.RA/0208229, math.RT/0305434. This is a family of commutative rings…
Cluster algebras III: Upper bounds and double Bruhat cells
Arkady Berenstein, Sergey Fomin, Andrei Zelevinsky
We continue the study of cluster algebras initiated in math.RT/0104151 and math.RA/0208229. We develop a new approach based on the notion of an upper cluster algebra, defined as an…
Tensor product multiplicities, canonical bases and totally positive varieties
Arkady Berenstein, Andrei Zelevinsky
We obtain a family of explicit "polyhedral" combinatorial expressions for multiplicities in the tensor product of two simple finite-dimensional modules over a complex semisimple Li…
Geometric and unipotent crystals
Arkady Berenstein, David Kazhdan
In this paper we introduce geometric crystals and unipotent crystals which are algebro-geometric analogues of Kashiwara's crystal bases. Given a reductive group G, let I be the set…
Coadjoint orbits, moment polytopes, and the Hilbert-Mumford criterion
Arkady Berenstein, Reyer Sjamaar
Consider a compact Lie group and a closed subgroup. Generalizing a result of Klyachko, we give a necessary and sufficient criterion for a coadjoint orbit of the subgroup to be cont…