Alladi Ramakrishnan Hall

Gelfand-Tsetlin patterns

S. Viswanath

IMSc

Classical Gelfand-Tsetlin patterns index a basis of finite dimensional irreducible representations of the general linear Lie algebra. I will describe the corresponding picture for representations of the corresponding "current algebra", where a distinguished class of representations (the so-called local Weyl modules) admit a basis parametrized by "Partition overlaid patterns" which are essentially Gelfand-Tsetlin patterns with additional overlay data consisting of a tuple of partitions fitting into rectangles of appropriate sizes determined by the entries of the pattern. This interpretation leads to many interesting consequences for classical GT patterns.