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.