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Washington State University

Combinatorics, Linear Algebra and Number Theory (CLaN) Seminar

Department of Mathematics

Neill Hall 5W

April 20, Monday, 4:10 - 5:00 PM

Alex Woo

Department of Mathematics

University of Idaho

Combinatorics, Linear Algebra and Number Theory (CLaN) Seminar

Department of Mathematics

Neill Hall 5W

April 20, Monday, 4:10 - 5:00 PM

Alex Woo

Department of Mathematics

University of Idaho

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

Abstract: Let G=GL(p+q, C) and K=GL(p, C)xGL(q, C). 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 can be naturally indexed by combinatorial objects known as clans. The geometry of orbit closures is studied both for their intrinsic interest and because of applications to the representation theory of the real Lie group U(p,q).

I will give an overview of these objects and their study as well as present some results relating the geometry of an orbit closure to the combinatorics of the indexing clan. In particular, local properties are governed by the combinatorial notion of pattern avoidance. This is based on joint work with Ben Wyser and Alexander Yong.

Abstract: Let G=GL(p+q, C) and K=GL(p, C)xGL(q, C). 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 can be naturally indexed by combinatorial objects known as clans. The geometry of orbit closures is studied both for their intrinsic interest and because of applications to the representation theory of the real Lie group U(p,q).

I will give an overview of these objects and their study as well as present some results relating the geometry of an orbit closure to the combinatorics of the indexing clan. In particular, local properties are governed by the combinatorial notion of pattern avoidance. This is based on joint work with Ben Wyser and Alexander Yong.