12,449 research outputs found
Virtual Braids
In the present paper we give a new method for converting virtual knots and
links to virtual braids. Indeed the braiding method given in this paper is
quite general, and applies to all the categories in which braiding can be
accomplished. We give a unifying topological interpretation of virtuals and
flats (virtual strings) and their isotopies via ribbon surfaces and abstract
link diagrams. We also give reduced presentations for the virtual braid group,
the flat virtual braid group, the welded braid group and several other
categories of braids. The paper includes a discussion of the topological
intepretation of the welded braid group in terms of tubes embedded in
four-space. A sequel to this paper will give a new proof of a Markov Theorem
for virtual braids (and related categories) via the L-move (a technique
pioneered for classical braids and braids in three-manifolds by the second
author).Comment: 31 pages, 22 figures, LaTeX documen
Representation theory of the Yokonuma-Hecke algebra
We develop an inductive approach to the representation theory of the
Yokonuma-Hecke algebra , based on the study of the spectrum
of its Jucys-Murphy elements which are defined here. We give explicit formulas
for the irreducible representations of in terms of standard
-tableaux; we then use them to obtain a semisimplicity criterion. Finally,
we prove the existence of a canonical symmetrising form on
and calculate the Schur elements with respect to that form.Comment: 28 page
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