• Title/Summary/Keyword: pure braid group

Search Result 2, Processing Time 0.015 seconds

REPRESENTATIONS OF THE BRAID GROUP $B_4$

  • Lee, Woo
    • Journal of the Korean Mathematical Society
    • /
    • v.34 no.3
    • /
    • pp.673-693
    • /
    • 1997
  • In this work, the irreducible complex representations of degree 4 of $B_4$, the braid group on 4 strings, are classified. There are 4 families of representations: A two-parameter family of representations for which the image of $P_4$, the pure braid group on 4 strings, is abelian; two families of representations which are the composition of an irreducible representation of $B_3$, the braid group on 3 strings, with a certain special homomorphism $\pi : B_4 \longrightarrow B_3$; a family of representations which are the tensor product of 2 irreducible two-dimensional representations of $B_4$.

  • PDF