**SMS scnews item created by James East at Mon 15 Nov 2010 1503**

Type: Seminar

Distribution: World

Expiry: 19 Nov 2010

**Calendar1: 19 Nov 2010 1205-1255**

**CalLoc1: Carslaw 175**

Auth: jamese@bari.maths.usyd.edu.au

### Algebra Seminar

# Diagonal reduction algebras

### Oleg Ogievetsky

#### Friday November 19, 12:05--12:55pm, Carslaw 175

###### Abstract

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.

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After the seminar we will take the speaker to lunch.

See the Algebra Seminar web page for information about other seminars in the series.

James East james.east@sydney.edu.au