Shuffle algebra, Macdonald operators and lattice models
The commutative (trigonometric) shuffle algebra is known to be isomorphic to the ring of symmetric functions (arxiv.org/abs/0904.2291v1). In this isomorphism one writes an integral operator where the shuffle algebra element stands as a kernel and the symmetric function gives the eigenvalues of this operator. The eigenvectors of these integral operators are the Macdonald functions. I will explain this construction and then discuss some applications.
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