The many integral graded cellular bases of Hecke algebras of complex reflection groups
C. Bowman
Abstract
We settle several long-standing problems in the theory of cyclotomic Hecke algebras: for each charge we construct the integral cellular basis predicted by Ariki's categorification theorem. We hence prove unitriangularity of decomposition matrices and Martin--Woodcock's conjecture.
Topics & Concepts
CategorificationMathematicsPure mathematicsConstruct (python library)ConjectureAlgebra over a fieldDecompositionReflection (computer programming)Basis (linear algebra)Hecke algebraGeometryComputer scienceBiologyProgramming languageEcologyAlgebraic structures and combinatorial modelsAdvanced Algebra and GeometryAdvanced Combinatorial Mathematics