A Holstein-Primakoff and Dyson Realizations for the Lie Superalgebra gl(m/n+1)

Abstract

The known Holstein-Primakoff and Dyson realizations for the Lie algebras $gl(n+1),n=1,2,\dots$ in terms of Bose operators are generalized to the class of the Lie superalgebras $gl(m/n+1)$ for any $n$ and $m$. Formally the expressions are the same as for $gl(m+n+1)$, however both Bose and Fermi operators are involved.

TeX, 7 pages

References in corpus (2)

• Finite-dimensional representations of the quantum superalgebra $U_q[gl(n/m)]$ and related q-identities
• An Analogue of Holstein-Primakoff and Dyson Realizations for Lie Superalgebras. The Lie superalgebra sl(1/n)

Cited by in corpus (6)

• Polynomial super-gl(n) algebras
• The Inhomogeneous Invariance Quantum Supergroup of Supersymmetry Algebra
• Determinant Form of Correlators in High Rank Integrable Spin Chains via Separation of Variables
• A Dyson realization and a Holstein-Primakoff realization for the quantum superalgebra $U_q[gl(n/m)]$
• Representations of quantum superalgebra Uq[gl(2|1)] in a coherent state basis and generalization
• The $q$-boson-fermion realizations of quantum suprealgebra $U_q(gl(2/1))$