2017/11/06 by Rostislav Devyatov, Devyatov, Rostislav
Mathematics · #math.AG #math.RT
paper · pdf · doi:10.48550/arxiv.1711.02058
Let G/B be a flag variety over an arbitrary field, where G is a semisimple split algebraic group with a simply laced Dynkin diagram, and B is a Borel subgroup. We say that the product of several classes of Schubert divisors in the Chow ring is multiplicity-free if it is possible to multiply it by a Schubert class (not necessarily of a divisor) and get the class of a point. In the present paper we find all possible degrees (in the Chow ring) of multiplicity-free products of classes of Schubert divisors. Also, given a product of several classes of Schubert divisors, we can decompose it into a linear combination of classes of Schubert varieties with (as was known before) nonnegative coefficients. We study the coefficients in this linear combination and provide a criterion detecting if such a coefficient equals 1, is greater than 1, or equals zero (i.e. a Schubert variety is not actually present in the linear combination).