Total positivity in the space of maximal tori

TL;DR

This paper introduces and investigates the concept of total positivity within the set of maximal tori in a complex connected reductive group, expanding the understanding of positivity structures in algebraic groups.

Contribution

It defines the totally positive part of maximal tori in complex reductive groups and explores its properties, providing new insights into positivity in algebraic group theory.

Findings

Characterization of the totally positive part of maximal tori

Structural properties of the positive subset within the group

Connections to existing positivity theories in algebraic groups

Abstract

Let G be a connected reductive group over the complex numbers with a fixed pinning. We define and study the totally positive part of the set of maximal tori of G.