Resumen de Twisted Schubert polynomials

Ricky Ini Liu

• We prove that twisted versions of Schubert polynomials defined by Sw0 =xn−1 1xn−2 2 ··· xn−1 and Swsi = (si + ∂i)Sw are monomial positive and give a combinatorial formula for their coefficients. In doing so, we reprove and extend a previous result about positivity of skew divided difference operators and show how it implies the Pieri rule for Schubert polynomials. We also give positive formulas for double versions of the Sw as well as their localizations.