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

## TL;DR

This paper extends the Littlewood-Richardson rule to algebraic cobordism of Grassmannians, providing formulas for products of Schubert classes and exploring generalized Schubert polynomials for hyperbolic formal group laws.

## Contribution

It introduces a product formula for smooth Schubert varieties in algebraic cobordism and advances the theory of generalized Schubert polynomials for hyperbolic formal group laws.

## Key findings

- Product formula for smooth Schubert varieties in algebraic cobordism
- Results on generalized Schubert polynomials for hyperbolic formal group laws
- Progress towards a generalized Littlewood-Richardson rule

## 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 the grassmannian. We also establish some results for generalized Schubert polynomials for hyperbolic formal group laws.