On the Jucys-Murphy method and fusion procedure for the Sergeev superalgebra
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918146040922112 |
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| author | Kashuba, Iryna Molev, Alexander Serganova, Vera |
| author_facet | Kashuba, Iryna Molev, Alexander Serganova, Vera |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18096 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Jucys-Murphy method and fusion procedure for the Sergeev superalgebra Kashuba, Iryna Molev, Alexander Serganova, Vera Representation Theory Rings and Algebras 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. |
| title | On the Jucys-Murphy method and fusion procedure for the Sergeev superalgebra |
| topic | Representation Theory Rings and Algebras |
| url | https://arxiv.org/abs/2502.18096 |