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 CGLn(C)-modules and the restriction of simple CGLn(C)-modules to some Levi subgroup.
Now let F denote an algebraically closed field of characteristic p > 0 and let G:= GLn(F). In this case very little is known about composition factors of tensor products of simple FG-modules. However, it is thought that they may still be related to the composition factors of the restriction of simple FG-modules to some Levi subgroup. In this talk we will discuss a relationship of this kind for tensor products of simple FGLn(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