M. Shapiro

activity

19982003

most citedCluster algebras and Weil-Petersson forms

5 citations · 5 across the 4 of their papers we have counts for

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3 papers · 1 filter

math.AG2001

The number of connected components in the double Bruhat cells for nonsimply-laced groups

Michael Gekhtman, Michael Shapiro, Alek Vainshtein

We compute the number of connected components in a generic real double Bruhat cell for series $B_{n}$ and $C_{n}$ and an exceptional group $F_{4}$ .

math.AG1999

Simply-laced Coxeter groups and groups generated by symplectic transvections

Boris Shapiro, Michael Shapiro, Alek Vainshtein +1

Let W be an arbitrary Coxeter group of simply-laced type (possibly infinite but of finite rank), u,v be any two elements in W, and i be a reduced word (of length m) for the pair (u…

math.AG1998

Skew-symmetric Vanishing Lattices and Intersections of Schubert Cells

B. Shapiro, M. Shapiro, A. Vainshtein

We prove that the number of connected components in the intersection of two open opposite Schubert cells in the variety of complete real n-dimensional flags equals 3*2^{n-1} for n>…