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Minimum Quantum Degrees for Isotropic Grassmannians in Types B and C

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arxiv 2004.00084 v4 pith:VSSURQXG submitted 2020-03-31 math.AG

Ryan M. Shifler , Camron Withrow This is my paper · ORCID
classification math.AG
keywords curvegrassmanniansisotropicminimumneighborhoodspartitionsquantumtypes
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abstract

We give a formula in terms of Young diagrams to calculate the minimum positive integer $d$ such that $q^d$ appears in the quantum product of two Schubert classes for the submaximal isotropic Grassmannians in Types B and C. We do this by studying curve neighborhoods. We compute curve neighborhoods in several combinatorial models including $k$-strict partitions and a set of partitions where their inclusion is compatible with the Bruhat order.

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