Irreducible representations of welded braid group

2024/12/30 by Inna Sysoeva, Sysoeva, Inna · 1 citation
Computer Science · Engineering · #20F36 #3D Shape Modeling and Analysis #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #FOS: Mathematics #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2412.21133

openalex publication_date 2024/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study irreducible matrix representations of the welded braid group WB_n, also known as the group of conjugating automorphisms of a free group F_n. We prove that WB_n has no irreducible representations of dimension r, where 2\leqslant r\leqslant n-2 for n\geqslant 5. We give complete classification of all extensions of irreducible representations of the braid group B_n to the welded braid group WB_n of dimensions n-1 (for n\geqslant 7) and n (for n\geqslant 7, n≠ 8). Classification of all extensions of the irreducible n-1- dimensional reduced Burau representation is given for n\geqslant 5, n≠ 6. A new one-parameter family of n-1- dimensional irreducible representations of WB_n is discovered. Classification of all extensions of the irreducible n-dimensional standard representation (also known as Tong-Yang-Ma representation) is given for all n\geqslant 3. New families of the 3-dimensional irreducible representations of WB₃ are discovered.

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• On the irreducibility of singular braid group representations

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