#### Alladi Ramakrishnan Hall

#### Combinatorial proof of a representation-theoretic identity

#### Rekha Biswal

##### IMSc

*An irreducible representation of a simple lie algebra has a basis called the Gelfand-Tsetlin basis which is parametrized by the points with integral co-ordinates in the Gelfand-Tsetlin polytope.*

Recently, Feigin, Fourier and Littelmann have found a different basis which was originally conjectured by Vinberg and is also parametrized by integral points in a certain polytope. In this talk, I will explain a combinatorial proof of the fact that both the Gelfand-Tsetlin polytope and the Feigin-Fourier-Littelmann-Vinberg polytope have the same number of integral points, a result which was recently proved by Ardila, Bliem and Salazar.

Done