**Date & Time:** April 17, 2013, 16:00-17:00.

**Venue:** Ramanujan Hall

**Title:**Unique factorization of tensor products for Kac-Moody algebras.

**Speaker: **Prof. R. Venkatesh, TIFR

**Abstract:**Suppose V is a finite dimensional representation of a complex simple Lie algebra that can be written as a tensor product of irreducible representations. A theorem of C.S. Rajan states that the irreducible factors that occur are uniquely determined, up to reordering, by the isomorphism class of V. I will present an elementary proof of Rajan's theorem, which generalizes with no extra effort to the infinite dimensional (Kac-Moody) Lie algebras. This is joint work with S. Viswanath.

Note: We are going to propose a new model for colloquium talks. This colloquium will start at 4.00 pm and will consist of two parts of 45 minutes each. In the first part the speaker will explain the motivation, statement etc. of the main result, after which we will have a break of 15 minutes for tea/snacks. Then the second part will start in which the speaker will explain the main ideas. If some member of the audience wants to leave after having tea/snacks, that will be ok, as the second part of the talk may be technical.