The degenerate analogue of Ariki’s categorification theorem

2008/12/31 by Jonathan Brundan, Alexander Kleshchev
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic structures and combinatorial models #Categorification #Conjecture #Degenerate energy levels #Duality (order theory) #Mathematics #Physics #Pure mathematics #math.RT #msc:17B20

paper · pdf · doi:10.1007/s00209-009-0603-y

published as Math. Z. 266 (2010), 877-919 · 44 pages

arxiv created 2008/12/31 · openalex publication_date 2009/09/10 · arxiv updated 2010/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We explain how to deduce the degenerate analogue of Ariki's categorification theorem over the ground field C as an application of Schur-Weyl duality for higher levels and the Kazhdan-Lusztig conjecture in finite type A. We also discuss some supplementary topics, including Young modules, tensoring with sign, tilting modules and Ringel duality.

Citations

• Koszul Duality Patterns in Representation Theory
• Affine sl_p controls the representation theory of the symmetric group and related Hecke algebras
• Canonical bases of q-deformed Fock spaces
• Cyclotomic q–Schur algebras
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