2022/08/06 by Kumar, Shrawan · 1 citation
#14C17 #14M17 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2208.03527
Following some work of Aluffi-Mihalcea-Schürmann-Su for the CSM classes of Schubert cells and some elaborate computer calculations by R. Rimanyi and L. Mihalcea, I conjecture that the CSM classes of the Richardson cells expressed in the Schubert basis have nonnegative coefficients. This conjecture was principally motivated by a new product \square coming from the Segre classes in the cohomology of flag varieties (such that the associated Gr of this product is the standard cup product) and the conjecture that the structure constants of this new product \square in the standard Schubert basis have alternating sign behavior. I prove that this conjecture on the sign of the structure constants of \square would follow from my above positivity conjecture about the CSM classes of Richardson cells.