Alladi Ramakrishnan Hall

Weyl modules associated to Kac-Moody algebras

Sachin Sharma

IIT Kanpur

Chari and Pressley defined the global Weyl modules, which are nothing but the maximal integrable highest weight modules for loop algebras. Local Weyl modules are the maximal finite dimensional quotients of global Weyl modules. Later, Feigin and Loktev generalized the notion of Weyl modules by replacing the Laurent polynomial ring by the algebra of functions on an affine variety.
    
In this talk, we extend the notion of local Weyl modules for a Lie algebra $\mathfrak{g} \times A$, where $\mathfrak{g}$ is any Kac-Moody algebra and $A$ is any finitely generated commutative associative algebra with unit over complex field, and prove a tensor decomposition theorem for local Weyl modules, thereby generalizing a result of  Chari and Pressley.