#### 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.*

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