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

Evgeny Feigin (Department of Mathematics, Higher School of Economics, National Research University, Moscow, Russia; and Skolkovo Institute of Science and Technology, Moscow, Russia)

Ievgen Makedonskyi (Max Planck Institute for Mathematics, Bonn, Germany; and Department of Mathematics, Higher School of Economics, National Research University, Moscow, Russia)

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.

Full Text (PDF format)

Received 9 July 2015

Published 1 September 2017