Alladi Ramakrishnan Hall

Area maximizing Gelfand-Tsetlin patterns

B Ravinder

IMSc

The Gelfand-Tsetlin polytope GT(lambda, mu) is a convex polytope
of triangular arrays with bounds lambda and weight mu. Recently we have defined an area (quadratic) function A on the GT(lambda, mu) related to the Chari-Loktev basis for the Weyl module W(lambda) of the Current algebra sl_n[t], and proved that it attains maximum at the unique point, further this point is integral.

In this talk we discuss how to get a monomial bases from the Gelfand-Tsetlin bases for the irreducibles of sl_n, extend it to get the Chari-Loktev basis and about the area maximizing Gelfand-Tsetlin patterns. This talk is based on joint work with K.N. Raghavan and S. Viswanath.