## University of Sydney Algebra Seminar

# Oleg Ogievetsky (Center of Theoretical Physics Luminy, Marseille, France)

## Friday 19th November, 12.05-12.55pm, Carslaw 175

### Diagonal reduction algebras

Let g be a Lie algebra and f its reductive Lie subalgebra. The branching rules of decompositions of g-modules into sums of f-modules are conveniently described with the help of a certain algebra, associated to the pair (g,f), called "reduction" algebra. I will illustrate on (possibly) simple examples the general structure of reduction algebras and tools to work with them. If time allows, I will say some words about diagonal reduction algebras which are related to decompositions of tensor products of irreps of reductive Lie algebras into the direct sums of irreps.