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Susan CooperCentral michigan university

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K-orbits on G/B, Richardson varieties, and a positive rule for (p,q)-Schubert constants

Ben WyserUniversity of georgia, athens

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For G a complex, reductive algebraic group, the fixed point subgroup of an involution of G is typically denoted K, and is referred to as a symmetric subgroup. K acts on the flag variety G/B (by left translations) with finitely many orbits. The geometry of such orbits and their closures is important in the infinite-dimensional representation theory of real forms of G.

One interesting example of a symmetric pair is (G,K) =(GL(p+q), GL(p) x GL(q)). Restricting attention to this example, I will discuss a recent result which establishes that a number of the K-orbit closures in this case coincide with certain Richardson varieties. When combined with a theorem of M. Brion on expressing the class of such an orbit closure in the Schubert basis, this observation implies a positive (in fact, multiplicity-free) rule for certain Schubert structure constants c_{u,v}^w --- those for which u,v form what I refer to as a "(p,q)-pair".

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Yorck Sommerhauseruniversity of south alabama

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Eugene GorskyStony Brook University

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SPRING BREAK

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Joerg Feldvossuniversity of South Alabama

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Cornelius PillenUniversity of South alabama

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