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math.QA2013★ 21 cited
Webs on surfaces, rings of invariants, and clusters
Sergey Fomin, Pavlo Pylyavskyy
We construct and study cluster algebra structures in rings of invariants of the special linear group action on collections of three-dimensional vectors, covectors, and matrices. Th…
math.QA1999★ 3 cited
Lecture notes on quantum cohomology of the flag manifold
Sergey Fomin
This is an exposition of some recent developments related to the object in the title, particularly the combinatorial computation of the (genus 0) Gromov-Witten invariants of the fl…
math.QA1998★ 12 cited
Mixed Bruhat operators and Yang-Baxter equations for Weyl groups
Francesco Brenti, Sergey Fomin, Alexander Postnikov
We introduce and study a family of operators which act in the span of a Weyl group and provide a multi-parameter solution to the quantum Yang-Baxter equations of the correspond…