559 citations · 1.2k across the 37 of their papers we have counts for
4 papers · 1 filter
Totally nonnegative and oscillatory elements in semisimple groups
Sergey Fomin, Andrei Zelevinsky
We generalize the well known characterizations of totally nonnegative and oscillatory matrices, due to F.R.Gantmacher, M.G.Krein, A.Whitney, C.Loewner, M.Gasca, and J.M.Pena to the…
Recognizing Schubert cells
Sergey Fomin, Andrei Zelevinsky
This paper focuses on the properties of Schubert cells as quasi-projective subvarieties of a generalized flag variety. More specifically, we investigate the problem of distinguishi…
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…
Double Bruhat cells and total positivity
Sergey Fomin, Andrei Zelevinsky
We study intersections of opposite Bruhat cells in a semisimple complex Lie group, and associated totally nonnegative varieties.