Anne Dranowski, IAS – Geometric Methods in Representation Theory Seminar

Title: How to compute the fusion product of MV cycles in type A

Abstract: In their recent paper on the MV basis and DH measures, Baumann, Kamnitzer and Knutson showed that Mirkovic and Vilonen’s geometric Satake basis of singular algebraic cycles yields a biperfect basis of the coordinate ring of a unipotent subgroup. Moreover, they showed that the structure constants of multiplication of basis vectors in this ring are given by intersection forms. We present joint work in progress generalizing an isomorphism of Mirkovic and Vybornov towards effectively computing these intersections when G=GL_m. Time permitting we discuss alternate methods in the literature as well as applications.