2025/08/11 by Riccardo Biagioli, Biagioli, Riccardo, Luca Costantini +3
Mathematics · #Algebraic structures and combinatorial models #Advanced Combinatorial Mathematics #Advanced Algebra and Geometry
paper · pdf · doi:10.48550/arxiv.2508.08388
The star operation, originally introduced by Kazhdan and Lusztig, was later specialized by Ernst to the so-called weak star reduction on the set of fully commutative elements of a Coxeter group. In this paper, we classify the star and weak star irreducible fully commutative elements in Coxeter groups of affine types \widetildeBn+1 and \widetildeDn+2. Focusing then on the case of type \widetildeDn+2, we use the classification of star irreducible elements to provide a new proof of the faithfulness of a diagrammatic representation of the corresponding generalized Temperley-Lieb algebra, along with an explicit description of Lusztig's a-function.