$T$-root systems of exceptional flag manifolds. Classification and invariants

TL;DR

This paper classifies the T-root systems of flag manifolds associated with exceptional compact simple Lie groups, focusing on those with a second Betti number of at least 2, and explores their invariants.

Contribution

It provides a comprehensive classification of T-root systems for certain exceptional flag manifolds and analyzes their invariants, advancing understanding of their geometric and algebraic structure.

Findings

Complete classification of T-root systems for specified flag manifolds

Identification of invariants associated with these T-root systems

Insights into the structure of exceptional Lie group flag manifolds

Abstract

We classify the systems of $T$-roots of the flag manifolds $M$ of the exceptional compact simple Lie groups with the second Betti number $b_2(M)\ge2$.