Twists and singular vectors in ^sl(2|1) representations

Abstract

We propose new formulas for singular vectors in Verma modules over the affine Lie superalgebra $\widehat{sl}(2|1)$. We analyze the coexistence of singular vectors of different types and identify the twisted modules $N_{h,k;\theta }$ arising as submodules and quotient modules of $\widehat{sl}(2|1)$ Verma modules. We show that with the twists (spectral flow transformations) properly taken into account, a resolution of irreducible representations can be constructed consisting of only the $N_{h,k;\theta }$ modules.

amsart, times. 20pp