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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.17458 |
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| _version_ | 1866912870162235392 |
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| author | Milionis, Christoforos |
| author_facet | Milionis, Christoforos |
| contents | We use the Jucys-Murphy elements of the BMW algebra to show that its center over the complex numbers for almost all parameters making it semisimple is given by Wheel Laurent polynomials, a subalgebra of the symmetric Laurent polynomials in the JM elements. As an application, we give an Okounkov-Vershik like approach to its finite dimensional representations. In the non semisimple case related to the type B Lie algebras, the central subalgebra of Wheel Laurent polynomials is large enough to separate blocks of the BMW algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17458 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The center of the BMW algebras and an Okounkov-Vershik like approach Milionis, Christoforos Representation Theory Quantum Algebra We use the Jucys-Murphy elements of the BMW algebra to show that its center over the complex numbers for almost all parameters making it semisimple is given by Wheel Laurent polynomials, a subalgebra of the symmetric Laurent polynomials in the JM elements. As an application, we give an Okounkov-Vershik like approach to its finite dimensional representations. In the non semisimple case related to the type B Lie algebras, the central subalgebra of Wheel Laurent polynomials is large enough to separate blocks of the BMW algebras. |
| title | The center of the BMW algebras and an Okounkov-Vershik like approach |
| topic | Representation Theory Quantum Algebra |
| url | https://arxiv.org/abs/2512.17458 |