English

Quantum Q-systems and fermionic sums -- the non-simply laced case

Quantum Algebra 2020-12-24 v3 Combinatorics Representation Theory

Abstract

In this paper, we seek to prove the equality of the qq-graded fermionic sums conjectured by Hatayama et al. in its full generality, by extending the results of Di Francesco and Kedem to the non-simply laced case. To this end, we will derive explicit expressions for the quantum QQ-system relations, which are quantum cluster mutations that correspond to the classical QQ-system relations, and write the identity of the qq-graded fermionic sums as a constant term identity. As an application, we will show that these quantum QQ-system relations are consistent with the short exact sequence of the Feigin-Loktev fusion product of Kirillov-Reshetikhin modules obtained by Chari and Venkatesh.

Keywords

Cite

@article{arxiv.1903.11492,
  title  = {Quantum Q-systems and fermionic sums -- the non-simply laced case},
  author = {Mingyan Simon Lin},
  journal= {arXiv preprint arXiv:1903.11492},
  year   = {2020}
}

Comments

43 pages. Typographical errors are corrected, and the references are clarified

R2 v1 2026-06-23T08:21:02.656Z