Extensions between Verma modules for dihedral groups

2017/12/14 by Gurbir Dhillon, Dhillon, Gurbir, Visu Makam +1
Mathematics · #17B10 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1712.05299

openalex publication_date 2017/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Computing the extensions between Verma modules is in general a very difficult problem. Using Soergel bimodules, one can construct a graded version of the principal block of Category O for any finite coxeter group. In this setting, we compute the extensions between Verma modules for dihedral groups.

Related

• Extensions of Verma modules
• A Hom formula for Soergel modules
• Constructing homomorphisms between Verma modules
• Categorification of Verma modules and indecomposable projective modules in the category \mathcal I_\mathfrakg(\mathfraksl₂) for \mathfraksl₂
• The category O for a general Coxeter system