### Miriam Norris

University of Manchester

Thursday 26 October 2023, 4.00pm – 5.00pm

Lecture Theatre D (Mathematical Institute)

**On composition factors for tensor products of simple GL(n) representations**

Understanding the composition factors of tensor products is an important question in representation theory. The classical Littlewood-Richardson coefficients describe the composition factors of both the tensor products of simple **C**GL_{n}(**C**)-modules and the restriction of simple **C**GL_{n}(**C**)-modules to some Levi subgroup.

Now let **F** denote an algebraically closed field of characteristic p > 0 and let G:= GL_{n}(**F**). In this case very little is known about composition factors of tensor products of simple **F**G-modules. However, it is thought that they may still be related to the composition factors of the restriction of simple **F**G-modules to some Levi subgroup. In this talk we will discuss a relationship of this kind for tensor products of simple **F**GL_{n}(**F**)-modules with the wedge square of the dual natural module and see how this might be used to find composition factors.

series: Pure Mathematics Colloquium

organiser: Scott Harper