2000/02/16 by Matthew G. Zinno, Zinno, Matthew G. · 1 citation
Mathematics · #16K20 (Secondary) #20F36 (Primary) 20C15 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Representation Theory (math.RT) #math.AT #math.GR #math.GT #math.RT #msc:16K20 #msc:20C15 #msc:20F36
paper · pdf · doi:10.48550/arxiv.math/0002136
15 pages, 4 figures. Submitted to Math Research Letters
arxiv created 2000/02/16 · openalex publication_date 2000/02/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A connection is made between the Krammer representation and the Birman-Murakami-Wenzl algebra. Inspired by a dimension argument, a basis is found for a certain irrep of the algebra, and relations which generate the matrices are found. Following a rescaling and change of parameters, the matrices are found to be identical to those of the Krammer representation. The two representations are thus the same, proving the irreducibility of one and the faithfulness of the other.