A class of representations of the ℤ₂×ℤ₂-graded special linear Lie superalgebra \mathfraksl(m₁+1,m₂|n₁,n₂) and quantum statistics

2025/06/30 by Stoilova, N. I., Van der Jeugt, J.
#FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2506.23953

Abstract

The description of the ℤ₂×ℤ₂-graded special linear Lie superalgebra \mathfraksl (m₁+1,m₂|n₁,n₂) is carried out via generators a₁^±,…, a_m1+m2+n1+n2^± that satisfy triple relations and are called creation and annihilation operators. With respect to these generators, a class of Fock type representations of \mathfraksl (m₁+1,m₂|n₁,n₂) is constructed. The properties of the underlying statistics are discussed and its Pauli principle is formulated.

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