Bases for the global Weyl modules of $\mathfrak{sl}_n$ of highest weight $m\omega_1$

Abstract

We utilize a theorem of B. Feigin and S. Loktev to give explicit bases for the global Weyl modules for the map algebras of the form ${\mathfrak{s}\mathfrak{l}}_n\otimes A$ of highest weight $m{\omega }_1$. These bases are given in terms of specific elements of the universal enveloping algebra, $U\left({\mathfrak{s}\mathfrak{l}}_n\otimes A\right)$, acting on the highest weight vector.