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arXiv · 2502.18096

On the Jucys-Murphy method and fusion procedure for the Sergeev superalgebra

Iryna Kashuba·Alexander Molev·Vera Serganova
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Abstract

We use the Jucys-Murphy elements to construct a complete set of primitive idempotents for the Sergeev superalgebra ${\mathcal S}_n$. We produce seminormal forms for the simple modules over ${\mathcal S}_n$ and over the spin symmetric group algebra with explicit constructions of basis vectors. We show that the idempotents can also be obtained from a new version of the fusion procedure.

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Iryna Kashuba, Alexander Molev, Vera Serganova. 2025-02-25. On the Jucys-Murphy method and fusion procedure for the Sergeev superalgebra. https://doi.org/10.1112/jlms.70302

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