Work

On the action of the Weyl group on canonical bases

Year: 2025

Type: article

Abstract: We study representations of simply-laced Weyl groups which are equipped with canonical bases. Our main result is that for a large class of representations, the separable elements of the Weyl group W act on these canonical bases by bijections up to lower-order terms. Examples of this phenomenon include the action of separable permutations on the Kazhdan–Lusztig basis of irreducible representations for the symmetric group, and the action of separable elements of W on dual canonical bases of weight zero in tensor product representations of a Lie algebra. Our methods arise from categorical representation theory, and in particular the study of the perversity of Rickard complexes acting on triangulated categories.

Source: Mathematische Zeitschrift

DOI: 10.1007/s00209-025-03709-7

Authors: Fern Gossow, Oded Yacobi

Institution: The University of Sydney

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: University of Sydney, Australian Research Council