**B. Ravinder **

TIFR

September 10, 2015

**On bases for local Weyl modules in type A**:
Let gg be a complex simple Lie algebra and gg[t]=gg otimes CC[t]
the corresponding current algebra. Local Weyl modules, introduced by Chari and Pressley, are interesting finite-dimensional gg[t]-modules.
Chari-Pressley also produced nice monomial bases for these modules in the case gg=sl_2. Later, Chari and Loktev clarified and extended the
construction of these bases to the case gg=sl_m. In joint work with K. N. Raghavan and S. Viswanath, we study stability of these bases for natural inclusions of local Weyl modules. We also introduce the notion of "partition overlay pattern" (POP) to reinterpret the indexing set of these bases. The notion of a POP leads naturally to the notion of the "area" of a Gelfand-Tsetlin pattern, and we prove that there exists a unique Gelfand-Tsetlin pattern of maximum area among all those with fixed bounding sequence and weight.