A quaternionic braid representation (after Goldschmidt and Jones) | Zendy

Eric C. Rowell | Zendy

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A quaternionic braid representation (after Goldschmidt and Jones)

Author(s) -

Eric C. Rowell

Publication year - 2011

Publication title -

quantum topology

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.763

H-Index - 16

eISSN - 1663-487X

pISSN - 1664-073X

DOI - 10.4171/qt/18

Subject(s) - braid , mathematics , braid group , representation (politics) , braid theory , algebra over a field , pure mathematics , quaternionic representation , real representation , history , irreducible representation , political science , law , archaeology , politics

We show that the braid group representations associated with the $(3,6)$-quotients of the Hecke algebras factor over a finite group. This was known to experts going back to the 1980s, but a proof has never appeared in print. Our proof uses an unpublished quaternionic representation of the braid group due to Goldschmidt and Jones. Possible topological and categorical generalizations are discussed.

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