Intersections of Schubert cells, and groups generated by symplectic
transvections
Michael Shapiro
Royal Insitute of Technology, Stockholm.
November 25,
4:15pm
refreshments at 3:45pm
2338
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 onetoone 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(atsign)math.mit.edu
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