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math.QA2011
Quantum cluster algebras and fusion products
Philippe Di Francesco, Rinat Kedem
-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 mut…
math.CO2011★ 52 cited
On the weighted enumeration of alternating sign matrices and descending plane partitions
Roger E. Behrend, Philippe Di Francesco, Paul Zinn-Justin
We prove a conjecture of Mills, Robbins and Rumsey [Alternating sign matrices and descending plane partitions, J. Combin. Theory Ser. A 34 (1983), 340-359] that, for any n, k, m an…
math-ph2011★ 3 cited
The solution of the quantum T-system for arbitrary boundary
Philippe Di Francesco, Rinat Kedem
We solve the quantum version of the -system by use of quantum networks. The system is interpreted as a particular set of mutations of a suitable (infinite-rank) quantum cl…