Contents Online
Mathematical Research Letters
Volume 24 (2017)
Number 3
Weyl modules for $\mathfrak{osp}(1, 2)$ and nonsymmetric Macdonald polynomials
Pages: 741 – 766
DOI: https://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.
Received 9 July 2015
Accepted 15 June 2016
Published 1 September 2017