T-systems and the pentagram map

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.

arXiv comment21 pages, contribution to FDIS13, July 2013

References in corpus (6)

• Functional Relations in Solvable Lattice Models I: Functional Relations and Representation Theory
• The q-characters of representations of quantum affine algebras and deformations of W-algebras
• Q-systems as cluster algebras II: Cartan matrix of finite type and the polynomial property
• Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras II: Types C_r, F_4, and G_2
• Liouville-Arnold integrability of the pentagram map on closed polygons
• Cluster X-varieties, amalgamation and Poisson-Lie groups

Cited by in corpus (3)

• Coxeter's frieze patterns at the crossroads of algebra, geometry and combinatorics
• Integrable cluster dynamics of directed networks and pentagram maps
• Projective Self-dual polygons in higher dimensions