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

Algebra Seminar

22nd March 2023, 2:30 pm – 3:30 pm

Fry Building, 2.04

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 FG-modules with the wedge square of the dual natural module and see how this might be used to find composition factors.

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