Let G be a finite-dimensional complex simple Lie algebra and G[t] be its current algebra. The degree grading on the polynomial ring gives a natural grading on G[t] and makes it a graded Lie algebra. Local Weyl modules introduced by Chari and Pressley are interesting finite-dimensional graded G[t]-modules. Corresponding to a dominant integral weight x of G there is a local Weyl module denoted by W(x). The zeroth graded piece of W(x) is the irreducible G-module V(x). In this talk, we discuss how to obtain a basis for W(x) from the basis of V(x) given by Gelfand-Tsetlin patterns, when G is of type A and C.

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Last updated: 29 Mar 2023