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Creators/Authors contains: "Simon Lin, Mingyan"

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  1. (, International Mathematics Research Notices)
    null (Ed.)
    Abstract In this paper, we seek to prove the equality of the $$q$$-graded fermionic sums conjectured by Hatayama et al. [ 14] in its full generality, by extending the results of Di Francesco and Kedem [ 9] 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 [ 5]. 
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