# Intersections of Schubert cells, and groups generated by symplectic transvections

## ABSTRACT

Starting from a reduced decomposition for an element $w$ of length $l$ in a Weyl group $W$, we define a particular subgroup of $G=GL_l(GF_2)$. The orbits of this subgroup (in the standard representation of $G$) are in one-to-one correspondence with connected components in the intersection of two open Schubert cells in a real flag manifold that have relative position $w$. Explicit description of these orbits allows us to calculate the number of connected components for most $w\in W$. This is joint work with B.Shapiro, A.Vainshtein and A.Zelevinsky

Speaker's Contact Info: mshapiro(at-sign)math.mit.edu