3 citations · 3 across the 3 of their papers we have counts for
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Redundancy in string cone inequalities and multiplicities in potential functions on cluster varieties
Gleb Koshevoy, Bea Schumann
We study defining inequalities of string cones via a potential function on a reduced double Bruhat cell. We give a necessary criterion for the potential function to provide a minim…
Combinatorics of canonical bases revisited: String data in type
Volker Genz, Gleb Koshevoy, Bea Schumann
We give a formula for the crystal structure on the integer points of the string polytopes and the -crystal structure on the integer points of the string cones of type for ar…
On the interplay of the parametrizations of canonical bases by Lusztig and string data
Volker Genz, Gleb Koshevoy, Bea Schumann
For arbitrary reduced words we give formulas for the crystal structures on string and Lusztig data of type A as well as the defining inequalities of the corresponding polytopes rev…
Polyhedral parametrizations of canonical bases & cluster duality
Volker Genz, Gleb Koshevoy, Bea Schumann
We establish the relation of the potential function constructed by Gross-Hacking-Keel-Kontsevich's and Berenstein-Kazhdan's decoration function on the open double Bruhat cell in th…