2017/04/01 by Philippe Di Francesco, Di Francesco, Philippe, Rinat Kedem +1
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1704.00154
openalex publication_date 2017/04/01 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
We introduce difference operators on the space of symmetric functions which\nare a natural generalization of the (q,t)-Macdonald operators. In the\nt\→\∞ limit, they satisfy the AN-1 quantum Q-system. We identify\nthe elements in the spherical AN-1 DAHA which are represented by these\noperators, as well as within the quantum toroidal algebra of gl1 and the\nelliptic Hall algebra. We present a plethystic, or bosonic, formulation of the\ngenerating functions for the generalized Macdonald operators, which we relate\nto recent work of Bergeron et al. Finally we derive constant term identities\nfor the current that allow to interpret them in terms of shuffle products. In\nparticular we obtain in the t\→\∞ limit a shuffle presentation of the\nquantum Q-system relations.\n