Dimension n Representations of the Braid Group on n Strings

2000/03/22 by Inna Sysoeva, Sysoeva, Inna · 1 citation
Mathematics · Physics and Astronomy · #20C #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20C

paper · pdf · doi:10.48550/arxiv.math/0003129

6 pages

arxiv created 2000/03/22 · openalex publication_date 2000/03/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1996 E. Formanek classified all the irreducible complex representations of B_n of dimension at most n-1, where B_n is the Artin braid group on n strings. In this paper we extend this classification to the representations of dimension n, for n≥ 9. We prove that all such representations are equivalent to a tensor product of a one-dimensional representation and a specialization of a certain one-parameter family of n-dimensional representations, that was first discovered in 1996 by Tong, Yang, and Ma. We use our classification of irreducible complex representations of corank two, in the preprint math.GR/0003047.

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