Weyl modules for the hyperspecial current algebra

Abstract

We develop the theory of global and local Weyl modules for the hyperspecial maximal parabolic subalgebra of type $A_{2n}^{(2)}$. We prove that the dimension of a local Weyl module depends only on its highest weight, thus establishing a freeness result for global Weyl modules. Furthermore, we show that the graded local Weyl modules are level one Demazure modules for the corresponding affine Lie algebra. In the last section we derive the same results for the special maximal parabolic subalgebras of the twisted affine Lie algebras not of type $A_{2n}^{(2)}$.

Cited by in corpus (6)

• Fusion products and toroidal algebras
• Twisted Demazure modules, fusion product decomposition and twisted Q--systems
• Twisted zastava and $q$-Whittaker functions
• Graded decompositions of fusion products in rank two
• Level one Weyl modules for toroidal Lie algebras
• Beilinson-Drinfeld Schubert varieties of parahoric group schemes and twisted global Demazure modules