Mingzhi Yang, part2, `Quantum Schubert calculus for smooth Schubert divisors in Fl_n' скачать в хорошем качестве

Mingzhi Yang, part2, `Quantum Schubert calculus for smooth Schubert divisors in Fl_n'

Abstract: In Schubert calculus, people study ring presentations of ordinary/quantum cohomology rings of flag varieties and multiplication rules for Schubert classes. Unlike ordinary cohomology, quantum Schubert calculus for Schubert varieties does not follow from that of flag varieties due to lack of functorial properties in quantum cohomology. Motivated by recent work on superpotentials for Schubert varieties of Li-Rietsch-Yang, we study quantum Schubert calculus for smooth Schubert divisors X in the complete flag varieties Fl_n. In a recent preprint Arxiv:2509-17857 by Li-Song-Xiong-Yang, we prove a Borel-type ring presentation of QH^*(X, \mathbb{Z}) and show that quantum Schubert polynomials defined by Fomin-Gelfand-Postnikov are representatives of Schubert classes in this ring presentation. We also give an Monk-Chevalley formula.