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Tuesday, May 21, 2019

**Abstract:** Every product of Schur functions arises as a Stanley symmetric function, which can be decomposed into Schur terms by Lascoux and Schutzenberger's transition recurrence, giving a Littlewood-Richardson rule as a special case. A similar approach using involution Stanley symmetric functions gives a Littlewood-Richardson rule for Schur P- and Q-functions. On the geometric side, Knutson, Lam, and Speyer showed that Stanley symmetric functions represent cohomology classes of graph Schubert varieties in Grassmannians. We identify analogous varieties in isotropic Grassmannians whose classes correspond to involution Stanley symmetric functions. We hope that this geometric connection will allow the transition approach to Littlewood-Richardson rules to be extended to the K-theory (and other cohomology theories) of isotropic Grassmannians.