Twisted Schubert polynomials
Abstract
We prove that twisted versions of Schubert polynomials defined by $\widetilde{\mathfrak S}_{w_0} = x_1^{n1}x_2^{n2} \cdots x_{n1}$ and $\widetilde{\mathfrak S}_{ws_i} = (s_i+\partial_i)\widetilde{\mathfrak S}_w$ 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 $\widetilde{\mathfrak S}_w$ as well as their localizations.
 Publication:

arXiv eprints
 Pub Date:
 May 2019
 DOI:
 10.48550/arXiv.1905.12839
 arXiv:
 arXiv:1905.12839
 Bibcode:
 2019arXiv190512839I
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Algebraic Geometry
 EPrint:
 19 pages