Smooth Schubert varieties and generalized Schubert polynomials in algebraic cobordism of Grassmannians

Jens Hornbostel and Nicolas Perrin

Vol. 294 (2018), No. 2, 401–422

DOI: 10.2140/pjm.2018.294.401

Abstract

We provide several ingredients towards a generalization of the Littlewood–Richardson rule from Chow groups to algebraic cobordism. In particular, we prove a simple product formula for multiplying classes of smooth Schubert varieties with any Bott–Samelson class in algebraic cobordism of Grassmannians. We also establish some results for generalized Schubert polynomials for hyperbolic formal group laws.

Keywords

Schubert calculus, cobordism, Grassmannian, generalized cohomology

Mathematical Subject Classification 2010

Primary: 14F43, 14M15, 14N15, 19L41, 55N22

Milestones

Received: 21 March 2017

Revised: 26 September 2017

Accepted: 3 November 2017

Published: 20 February 2018