B. Ravinder
TIFR
September 10, 2015
On bases for local Weyl modules in type A: Let $\mathfrak g$ be a complex simple Lie algebra and $\mathfrak g[t]=\mathfrak g \otimes \mathbb C[t]$ the corresponding current algebra. Local Weyl modules, introduced by Chari and Pressley, are interesting finite-dimensional $\mathfrak g[t]$-modules. Chari-Pressley also produced nice monomial bases for these modules in the case $\mathfrak g=sl_2$. Later, Chari and Loktev clarified and extended the construction of these bases to the case $\mathfrak g=sl_m$. 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.
TIFR
September 10, 2015
On bases for local Weyl modules in type A: Let $\mathfrak g$ be a complex simple Lie algebra and $\mathfrak g[t]=\mathfrak g \otimes \mathbb C[t]$ the corresponding current algebra. Local Weyl modules, introduced by Chari and Pressley, are interesting finite-dimensional $\mathfrak g[t]$-modules. Chari-Pressley also produced nice monomial bases for these modules in the case $\mathfrak g=sl_2$. Later, Chari and Loktev clarified and extended the construction of these bases to the case $\mathfrak g=sl_m$. 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.