Abstract
Following work of Brundan and Kleshchev (2000), which considered tensor products with the natural module (and its dual) for GL ( n ) , we take the next fundamental module and explore the relationship between multiplicities of composition factors of tensor products of simple modules for GL ( n ) and branching multiplicities. In doing this we provide a method for determining the composition multiplicities for some composition factors of tensor products of simple modules with the wedge square of the dual natural module.
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