2011/09/28 by Philippe Di Francesco, Di Francesco, Philippe, Rinat Kedem +1
Mathematics · Physics and Astronomy · #13F60 #17B37 #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math-ph #math.CO #math.MP #math.QA #math.RT #msc:13F60 #msc:17B37
paper · pdf · doi:10.48550/arxiv.1109.6261
43 pages
arxiv created 2011/09/28 · arxiv updated 2011/09/29
Q-systems are recursion relations satisfied by the characters of the restrictions of special finite-dimensional modules of quantum affine algebras. They can also be viewed as mutations in certain cluster algebras, which have a natural quantum deformation. In this paper, we explain the relation in the simply-laced case between the resulting quantum Q-systems and the graded tensor product of Feigin and Loktev. We prove the graded version of the M=N identities, and write expressions for these as non-commuting evaluated multi-residues of suitable products of solutions of the quantum Q-system. This leads to a simple reformulation of Feigin and Loktev's fusion coefficients as matrix elements in a representation of the quantum Q-system algebra.