Projective oscillator representations of orthogonal Lie algebras

2025/12/22 by Zhenyu Zhou
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Nonlinear Waves and Solitons #Algebraic structures and combinatorial models

paper · doi:10.1080/00927872.2025.2597885

Abstract

The projective transformations of n-dimensional space give rise to a one-parameter family of inhomogeneous first-order differential operator representations of sln+1. By restricting to the subalgebra on+1, we obtain new explicit representations for the simple Lie algebras of type B or type D. Applying these operators on the space of exponential-polynomial functions or partially swapping differential operators and multiplication operators, we realize more general explicit representations for on+1. All of these representation spaces are infinite-dimensional. We obtain the composition series of these on+1-modules under certain conditions.

Citations

• Q-analogues of Clifford and Weyl algebras-spinor and oscillator representations of quantum enveloping algebras
• Conformal oscillator representations of orthosymplectic Lie superalgebras
• Projective oscillator representations of sl(n+1|m) and osp(m|n+1)

Related

• Conformal Oscillator Representations of Orthogonal Lie Algebras
• Projective Oscillator Representations of sl(n+1) and sp(2m+2)
• Full Projective Oscillator Representations of Special Linear Lie Algebras and Combinatorial Identities
• Projective oscillator representations of sl(n+1|m) and osp(m|n+1)
• Full Conformal Oscillator Representations of Orthogonal Lie Algebras and Combinatorial Identities