Weyl modules for osp(1, 2) and nonsymmetric MacDonald polynomials

The main goal of our paper is to establish a connection between the Weyl modules of the current Lie superalgebras (twisted and untwisted) attached to osp(1, 2) and the nonsymmetric Macdonald polynomials of types A(2) 2 and A(2) 2 . We compute the dimensions and construct bases of the Weyl modules. We also derive explicit formulas for the t = 0 and t = ∞ specializations of the nonsymmetric Macdonald polynomials. We show that the specializations can be described in terms of the Lie superalgebras action on the Weyl modules.