JOINT MATHEMATICS COLLOQUIUM

UNIVERSITY OF IDAHO

WASHINGTON STATE UNIVERSITY


Department of Mathematics

University of Idaho


Spring 2015

Thursday,  February 5, 3:30-4:20 pm, room TLC 223

Refreshments in Brink 305 at 3:00 pm

Combinatorics of clans and geometry of B orbits on G/K

 

Alexander Woo


Department of Mathematics

University of Idaho

Abstract

Let G=GL(p+q) and K=GL(p)xGL(q).  The set of cosets of G/K has the structure of an algebraic variety.  Furthermore, the group B of upper triangular matrices acts on G/K with finitely many orbits.  These orbits have a simple description in terms of linear algebra and can be naturally indexed by a set of objects known as clans.

Various geometric properties of these B orbits (and their closures) can be read from combinatorial properties of the indexing clans.  In particular, clans admit a notion of pattern avoidance and some singularity properties of B orbit closures are characterized by pattern avoidance.

This is based on joint work in progress with Ben Wyser and Alexander Yong.