Parabolic Stabilization and Cutting for Reduction Superalgebras

2025/07/29 by Hartwig, Jonas T.
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2507.21595

Abstract

The diagonal reduction algebra of a reductive Lie algebra \mathfrakg is a localization of the Mickelsson algebra associated to the symmetric pair (\mathfrakg×\mathfrakg, \mathfrakg). In 2010, Khoroshkin and Ogievetsky introduced the methods of stabilization and cutting, which relate the commutation relations in the diagonal reduction algebra of \mathfrakgl_m⊕\mathfrakgl_n with those in the diagonal reduction algebra of \mathfrakgl_m+n. We extend this method to a wide range of reduction algebras, including all diagonal and differential reduction algebras for basic classical Lie superalgebras. We show how the method can be used for computing relations in the diagonal reduction algebra of \mathfrakso₈ and differential reduction algebra of \mathfraksp_2n.

Citations

• Exact Solutions to the Klein--Gordon Equation via Reduction Algebras
• Diagonal reduction algebra and reflection equation
• Diagonal reduction algebras of \gl type
• On the Ghost Centre of Lie Superalgebras

Related

• Diagonal reduction algebras of \gl type
• Diagonal reduction algebra and reflection equation
• Reduction theory for stably graded Lie algebras
• The variety of reductions for a reductive symmetric pair
• Mickelsson algebras and inverse Shapovalov form