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Explicit Construction of the Representation of the Braid Generator sigma Associated with the One-Parameter Family of Minimal Typical Highest Weight (0,0 | alpha) Representations of Uq[gl(2 | 1)
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The 'Links-Gould invariant' is a two-variable Laurent polynomial invariant of oriented (1,1) tangles, which is derived from the representation of the braid generator associated with the one-parameter family of four dimensional representations with highest weights (0,0|a) of the quantum superalgebra U_q[gl(2|1)]. We use an abstract tensor state model to evaluate the invariant, as per the construction of the bracket polynomial state model used by Louis Kauffman to derive the Jones polynomial. This model facilitates both computation and theoretical exploration.
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http://www.arxiv.org/abs/math.GT/9909063
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