# Determinantal and Tableau Formulas for Back-Stable Schubert Polynomials

Schubert polynomials of vexillary (2 1 4 3 avoiding) permutations are well known to have tableau and determinantal formulas. The goal of thistalk is to extend this to general permutations, by writing a generalSchubert polynomial as a sum of products of such determinants. Thisis based on the bumpless-pipe-dream formula of Lam, Lee, andShimozono. After reviewing some basic properties of back-stableSchubert polynomials, we’ll discuss determinantal and tableauformulas (some of which seem to be new), and then show how to usethese to decompose general Schubert polynomials. Anything originalis joint work with Dave Anderson.

**Date published:**Wednesday, April 12, 2023