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Macdonald Duality and the proof of the Quantum Q-system conjecture
Philippe Di Francesco, Rinat Kedem
The -symmetry of Cherednik's spherical double affine Hecke algebras in Macdonald theory includes a distinguished generator which acts as a discrete time evolution…
Quantum Q systems: From cluster algebras to quantum current algebras
Philippe Di Francesco, Rinat Kedem
In this paper, we recall our renormalized quantum Q-system associated with representations of the Lie algebra , and show that it can be viewed as a quotient of the quantum cur…
The Non-Commutative -system and its positive Laurent property
P. Di Francesco
We define a non-commutative version of the T-system, which underlies frieze patterns of the integer plane. This system has discrete conserved quantities and has a particular…
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…