I’ll explain the construction known as the Feigin-Loktev fusion product, which can be viewed as a grading on spaces of conformal blocks, coinvariant spaces, or simply a refinement of Clebsch-Gordan coefficients. I’ll give some applications to construction of representations of Kac-Moody algebras, the representation theory of finite-dimensional Lie algebras and explain the relation to the Kirillov-Reshetikhin conjecture for completeness of Bethe states in generalized Heisenberg models.

Dept of Mathematics, U.Illinois at Urbana-Champaign