Composition Multiplicities of Tensor Products and Branching Multiplicities for $\text{GL}(n)$
Abstract
Following work of Brundan and Kleshchev (2000), which considered tensor products with the natural module (and its dual) for $\text{GL}(n)$, we take the next fundamental module and explore the relationship between multiplicities of composition factors of tensor products of simple modules for $\text{GL}(n)$ 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2024
- DOI:
- 10.48550/arXiv.2410.03400
- arXiv:
- arXiv:2410.03400
- Bibcode:
- 2024arXiv241003400N
- Keywords:
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- Mathematics - Representation Theory;
- Mathematics - Group Theory