The cyclotomic BMW algebra associated with the two string type B braid group

2006/11/17 by Stewart Wilcox, Wilcox, Stewart, Shona Yu +1 · 1 citation
Mathematics · #17B37 #20F36 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0611518

openalex publication_date 2006/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The cyclotomic Birman-Murakami-Wenzl (or BMW) algebras B_n^k, introduced by R. Haring-Oldenburg, are extensions of the cyclotomic Hecke algebras of Ariki-Koike, in the same way as the BMW algebras are extensions of the Hecke algebras of type A. In this paper we focus on the case n=2, producing a basis of B₂^k and constructing its left regular representation.

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• Simple B₄ representations associated to cyclotomic Hecke algebras

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