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

• URL: http://arxiv.org/abs/2506.23953v1
• Date: Mon, 30 Jun 2025 15:21:04 GMT
• 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
• Authors: N. I. Stoilova, J. Van der Jeugt,
• Abstract summary: description of the $mathbbZtimesmathbbZ$-graded special linear Lie superalgebra.<n>Properties of the underlying statistics are discussed and its Pauli principle is formulated.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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