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.
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.