Ghost center and representations of the diagonal reduction algebra of \(\mathfrak{osp}(1 | 2)\)

DOI10.1016/j.geomphys.2023.104788OpenAlexW4321768860MaRDI QIDQ2696137

Jonas T. Hartwig, Dwight Anderson Williams II

Publication date: 6 April 2023

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.08068

zbMATH Keywords

representation theoryLie superalgebrareduction algebraghost centerZhelobenko algebra

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Universal enveloping (super)algebras (17B35) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Superalgebras (17A70)

Cites Work

• Representation rings of Lie superalgebras
• The enveloping algebra of the Lie superalgebra \(\mathfrak{osp}(1,2)\)
• On Casimir's ghost
• The minimal primitive spectrum of the enveloping algebra of the Lie superalgebra \(\text{osp}(1,2l)\).
• On the ghost centre of Lie superalgebras.
• Dynamical Weyl groups and applications
• Diagonal reduction algebra and the reflection equation
• Contravariant form for reduction algebras
• Step algebras of semi-simple subalgebras of Lie algebras
• Projection operators for simple Lie groups. II: General scheme for constructing lowering operators. The groups \(\mathrm{SU}(n)\)
• Mickelsson algebras and Zhelobenko operators.
• Extremal projector and dynamical twist
• Representations of centrally extended Lie superalgebra $\mathfrak {psl}(2|2)$psl(2|2)
• Generating functions for the ${\mathfrak{osp}}(1| 2)$ Clebsch–Gordan coefficients
• Extremal projections for reductive classical Lie superalgebras with a non-degenerate generalized Killing form
• Irreducible representations of the osp(2,1) and spl(2,1) graded Lie algebras
• A remark on the Casimir elements of Lie superalgebras and quantized Lie superalgebras
• Lie superalgebras
• Diagonal reduction algebra for $\mathfrak{osp}(1|2)$
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