Super tableaux and a branching rule for the general linear Lie superalgebra

Abstract

In this note, we formulate and prove a branching rule for simple polynomial modules of the Lie superalgebra . Our branching rules depend on the conjugacy class of a Borel subalgebra. A Gelfand–Tsetlin basis of a polynomial module associated to each Borel subalgebra is obtained in terms of generalized semistandard tableaux.

Keywords:

• duality
• Gelfand–Tsetlin bases
• Lie superalgebras
• representations
• Young diagrams

AMS Subject Classifications:

• 05E10
• 17B10

Acknowledgements

We are grateful to Weiqiang Wang for his suggestion for this collaboration, and for the guidance and advice he has given over the course of this project. We would also like to thank Shun-Jen Cheng for his many helpful conversations. The third author was supported by an REU under Wang’s NSF grant.