JOINT MATHEMATICS COLLOQUIUMUNIVERSITY OF IDAHOWASHINGTON STATE UNIVERSITY |
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Abstract |
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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.
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