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Title:
Duality in Macdonald theory and the q-Whittaker limit of spherical DAHAs
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Abstract:
We use a duality property of the spherical DAHA and the eigenfunctions of Macdonald polynomials to compute the relations satisfied by certain $\tau_+$-translated Macdonald and Koornwinder operators in the q-Whittaker limit. We find the subset of operators which satisfy the recursion relation known as the quantum Q-systems for root systems whose finite Weyl groups are of classical types, by making use of this duality. [Joint with P. Di Francesco]
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