A class of representations of the $\mathbb{Z}_2\times\mathbb{Z}_2$-graded special linear Lie superalgebra $\mathfrak{sl}(m_1+1,m_2|n_1,n_2)$ and quantum statistics
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| Format: | Preprint |
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2025
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| _version_ | 1866912458041458688 |
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| author | Stoilova, N. I. Van der Jeugt, J. |
| author_facet | Stoilova, N. I. Van der Jeugt, J. |
| contents | The description of the $\mathbb{Z}_2\times\mathbb{Z}_2$-graded special linear Lie superalgebra $\mathfrak{sl} (m_1+1,m_2|n_1,n_2)$ is carried out via generators $a_1^\pm,\ldots, a_{m_1+m_2+n_1+n_2}^\pm$ that satisfy triple relations and are called creation and annihilation operators. With respect to these generators, a class of Fock type representations of $\mathfrak{sl} (m_1+1,m_2|n_1,n_2)$ is constructed. The properties of the underlying statistics are discussed and its Pauli principle is formulated. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_23953 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A class of representations of the $\mathbb{Z}_2\times\mathbb{Z}_2$-graded special linear Lie superalgebra $\mathfrak{sl}(m_1+1,m_2|n_1,n_2)$ and quantum statistics Stoilova, N. I. Van der Jeugt, J. Mathematical Physics Quantum Physics The description of the $\mathbb{Z}_2\times\mathbb{Z}_2$-graded special linear Lie superalgebra $\mathfrak{sl} (m_1+1,m_2|n_1,n_2)$ is carried out via generators $a_1^\pm,\ldots, a_{m_1+m_2+n_1+n_2}^\pm$ that satisfy triple relations and are called creation and annihilation operators. With respect to these generators, a class of Fock type representations of $\mathfrak{sl} (m_1+1,m_2|n_1,n_2)$ is constructed. The properties of the underlying statistics are discussed and its Pauli principle is formulated. |
| title | A class of representations of the $\mathbb{Z}_2\times\mathbb{Z}_2$-graded special linear Lie superalgebra $\mathfrak{sl}(m_1+1,m_2|n_1,n_2)$ and quantum statistics |
| topic | Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2506.23953 |