Macdonald operators and quantum Q-systems for classical types

2019/08/02 by Di Francesco, Philippe, Kedem, Rinat
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1908.00806

Abstract

We propose solutions of the quantum Q-systems of types B_N,C_N,D_N in terms of q-difference operators, generalizing our previous construction for the Q-system of type A. The difference operators are interpreted as q-Whittaker limits of discrete time evolutions of Macdonald-van Diejen type operators. We conjecture that these new operators act as raising and lowering operators for q-Whittaker functions, which are special cases of graded characters of fusion products of KR-modules.

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