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

Mathematical Research Letters. 2017. Vol. 24. No. 3. P. 741-766.

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 $\mosp(1,2)$ and the nonsymmetric Macdonald polynomials of types $A_2^{(2)}$
and $A_2^{(2)\dagger}$. We compute the dimensions and construct bases of the Weyl modules.
We also derive explicit formulas for the $t=0$ and $t=\infty$ 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.