T-systems and the pentagram map

TL;DR

This paper explores the mathematical relationships between the $A_d$ $T$-system, the octahedron relation, and the pentagram map, highlighting their integrable structures and generalizations.

Contribution

It uncovers new connections between discrete integrable systems and geometric transformations, expanding understanding of their underlying algebraic and geometric properties.

Findings

Identifies links between $A_d$ $T$-system and pentagram map

Shows integrability properties of these systems

Generalizes the pentagram map to broader contexts

Abstract

These notes summarize two different connections between two discrete integrable systems, the $A_d$ $T$-system and its infinite-rank analog, the octahedron relation, and the pentagram map and its various generalizations.