Communications in Algebra· 2026Q2
Star and weak star irreducible fully commutative elements in Coxeter groups of affine types B and D
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- 2026year
Short summary
This paper classifies star and weak star irreducible fully commutative elements in Coxeter groups of affine types B~n+1 and D~n+2, providing a new proof for the faithfulness of a diagrammatic representation of the generalized Temperley–Lieb algebra for type D~n+2.
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Key points
- Classifies star and weak star irreducible fully commutative elements in Coxeter groups of affine types B~n+1 and D~n+2.
- Focuses on type D~n+2 to provide a new proof for the faithfulness of a diagrammatic representation of the generalized Temperley–Lieb algebra.
- Offers an explicit description of Lusztig’s a-function for type D~n+2.
AI-generated from the title and abstract; the full text is not read.
Abstract
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 B~n+1 and D~n+2. Focusing then on the case of type D~n+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.
The authors' abstract, as published at the source. Communications in Algebra, 2026 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics