Ada Stelzer, `Gröbner crystal structures' скачать в хорошем качестве

Ada Stelzer, `Gröbner crystal structures'

Abstract: A Gröbner crystal structure (GCS) for an ideal J in a polynomial ring S is a crystal graph on the monomials of S that restricts to a crystal graph on the standard monomials of J with respect to some term order. An explicit GCS for a given J yields a combinatorial rule for the irreducible representation multiplicities (i.e., the equivariant Hilbert series) of J or of S/J. In this talk we develop a GCS for determinantal ideals in the space C[Matm, n] of matrices, using the crystal structure of Danilov-Koshevoi and van Leeuwen. Our GCS applies to Schubert determinantal ideals and many other ideals in algebraic combinatorics, giving a generalized Littlewood-Richardson rule for their equivariant Hilbert series via the Robinson-Schensted-Knuth (RSK) correspondence. This talk is based on joint work with Abigail Price and Alexander Yong.