Bases for the Global Weyl modules of $\mathfrak{sl}_n$ of highest weight $mω_1$

Samuel Chamberlin, Amanda Croan

Published 2015-06-29Version 1

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 $\mathfrak{sl}_n\otimes A$ of highest weight $m\omega_1$. These bases are given in terms of specific elements of the universal enveloping algebra, $\mathbf{U}(\mathfrak{sl}_n\otimes A)$, acting on the highest weight vector.