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Representations of the Necklace Braid Group N Bn of Dimension 4 (n = 2, 3, 4)

Abstract

We consider the irreducible representations each of dimension 2 of the necklace braid group NBn (n = 2; 3; 4). We then consider the tensor product of the representations of NBn (n = 2; 3; 4) and determine necessary and sucient condition under which the constructed representations are irreducible. Finally, we determine conditions under which the irreducible representations of NBn (n = 2; 3; 4) of degree 2 are unitary relative to a hermitian positive definite matrix.

Journal/Conference Information

Arabian Journal of Mathematics,DOI: https://doi.org/10.1007/s40065-021-00325-1, ISSN: 2193-5351, Volume: 10, Issue: 2, Pages Range: 1-21,