2019/03/27 by Lin, Mingyan Simon
#13F60 #17B37 #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1903.11492
In this paper, we seek to prove the equality of the q-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 Q-system relations, which are quantum cluster mutations that correspond to the classical Q-system relations, and write the identity of the q-graded fermionic sums as a constant term identity. As an application, we will show that these quantum Q-system relations are consistent with the short exact sequence of the Feigin-Loktev fusion product of Kirillov-Reshetikhin modules obtained by Chari and Venkatesh.