Unitary representations of cyclotomic Hecke algebras at roots of unity: combinatorial classification and BGG resolutions

2021/07/02 by C. Bowman, Bowman, Chris, Emily Norton +3
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2107.01190

openalex publication_date 2021/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We relate the classes of unitary and calibrated representations of cyclotomic Hecke algebras and, in particular, we show that for the most important deformation parameters these two classes coincide. We classify these representations in terms of both multipartition combinatorics and as the points in the fundamental alcove under the action of an affine Weyl group. Finally, we cohomologically construct these modules via BGG resolutions.

Related

• Lectures on cyclotomic Hecke algebras
• Semisimple representations of alternating cyclotomic Hecke algebras
• Modular representations of cyclotomic Hecke algebras of type G(r,p,n)
• Jucys--Murphy elements and representations of cyclotomic Hecke algebras
• Simple B₄ representations associated to cyclotomic Hecke algebras