The atomic Leibniz rule

TL;DR

This paper generalizes the twisted Leibniz rule for Demazure operators to atomic double cosets and links it to a polynomial forcing property in singular Soergel bimodules, advancing algebraic understanding.

Contribution

It introduces a new atomic Leibniz rule for Demazure operators associated with atomic double cosets, connecting it to singular Soergel bimodules.

Findings

Established the atomic Leibniz rule for Demazure operators.

Proved the equivalence to a polynomial forcing property.

Enhanced the theoretical framework of singular Soergel bimodules.

Abstract

The Demazure operator associated to a simple reflection satisfies the twisted Leibniz rule. In this paper we introduce a generalization of the twisted Leibniz rule for the Demazure operator associated to any atomic double coset. We prove that this atomic Leibniz rule is equivalent to a polynomial forcing property for singular Soergel bimodules.