Work

Flat degenerations of flag supermanifolds for basic Lie superalgebras

Year: 2026

Type: article

Abstract: Motivated by bases of representations compatible with the PBW filtration for basic Lie superalgebras by Kus and Fourier, we generalise the construction of degenerations of flag varieties via favourable modules to the super setup. In the classical setup, this method of degenerating flag varieties by Feigin, Fourier and, Littelmann relies on constructing bases of representations of Lie algebras such that in the coordinate ring of an embedded flag varietiy their multiplication can be identified with an affine semigroup modulo terms of higher degree. By killing off said terms of higher degree via a filtration construction, one gets a toric variety the embedded flag variety degenerates into. By adapting these techniques we provide a similar construction and discuss when one can get a degeneration into a toric supervariety, as defined by Jankowski

Source: Journal of Pure and Applied Algebra

DOI: 10.1016/j.jpaa.2026.108271

Author: Ibrahim Ahmad

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funder: Deutsche Forschungsgemeinschaft

Award: TRR 195: Symbolische Werkzeuge in der Mathematik und ihre Anwendung