Representations of Hecke algebras and the Alexander polynomial
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Date
2010-06
Authors
Black, Samson, 1979-
Journal Title
Journal ISSN
Volume Title
Publisher
University of Oregon
Abstract
We study a certain quotient of the Iwahori-Hecke algebra of the symmetric group Sd , called the super Temperley-Lieb algebra STLd. The Alexander polynomial of a braid can be computed via a certain specialization of the Markov trace which descends to STLd. Combining this point of view with Ocneanu's formula for the Markov trace and Young's seminormal form, we deduce a new state-sum formula for the Alexander polynomial. We also give a direct combinatorial proof of this result.
Description
viii, 50 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number.
Keywords
Hecke algebras, Alexander polynomal, Symmetric groups, Markov trace, Mathematics, Theoretical mathematics