Root operators, root groups and retractions

TL;DR

This paper demonstrates that Gaussent--Littelmann root operators on galleries can be represented using retractions in Bruhat-Tits buildings and explores their relation to the root datum at infinity.

Contribution

It provides a new purely geometric interpretation of root operators via retractions, linking combinatorial and geometric structures in buildings.

Findings

Root operators expressed through retractions in buildings

Connection established between root operators and root datum at infinity

Enhances understanding of geometric representation theory

Abstract

We prove that the Gaussent--Littelmann root operators on galleries can be expressed purely in terms of retractions of a (Bruhat-Tits) building. In addition we establish a connection to the root datum at infinity.