2025/04/08 by Leonardo Patimo, Patimo, Leonardo
Mathematics · #Advanced Combinatorial Mathematics #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2504.06161
openalex publication_date 2025/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study Soergel modules for arbitrary Coxeter groups. For infinite Coxeter groups, we show that the homomorphisms between Soergel modules are in general more than those coming from morphisms of Soergel bimodules. This result provides a negative answer to a question posed by Soergel. We further show that the dimensions of the morphism spaces agree with the pairing in the Hecke algebra when Soergel modules are instead regarded as modules over the structure algebra. Moreover, we use this module structure to define a distinguished submodule of indecomposable Soergel bimodules that mimics the cohomology submodule of the intersection cohomology. Combined with the Hodge theory of Soergel bimodules, this can be used to extend results regarding the shape of Bruhat intervals, such as top-heaviness, to arbitrary Coxeter groups.