English

T-systems and Y-systems for quantum affinizations of quantum Kac-Moody algebras

Quantum Algebra 2010-01-15 v3

Abstract

The T-systems and Y-systems are classes of algebraic relations originally associated with quantum affine algebras and Yangians. Recently the T-systems were generalized to quantum affinizations of a wide class of quantum Kac-Moody algebras by Hernandez. In this note we introduce the corresponding Y-systems and establish a relation between T and Y-systems. We also introduce the T and Y-systems associated with a class of cluster algebras, which include the former T and Y-systems of simply laced type as special cases.

Keywords

Cite

@article{arxiv.0909.4618,
  title  = {T-systems and Y-systems for quantum affinizations of quantum Kac-Moody algebras},
  author = {Atsuo Kuniba and Tomoki Nakanishi and Junji Suzuki},
  journal= {arXiv preprint arXiv:0909.4618},
  year   = {2010}
}

Comments

23 pages; the final (journal) version published in SIGMA