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# Mathematical Research Letters

## Volume 24 (2017)

### Number 3

### Weyl modules for $\mathfrak{osp}(1, 2)$ and nonsymmetric Macdonald polynomials

Pages: 741 – 766

DOI: http://dx.doi.org/10.4310/MRL.2017.v24.n3.a6

#### Authors

#### Abstract

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 $\mathfrak{osp}(1, 2)$ and the nonsymmetric Macdonald polynomials of types $A^{(2)}_2$ and $A^{(2)\dagger}_2$. 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.

Paper received on 9 July 2015.