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Dimension n Representations of the Braid Group on n Strings

โœ Scribed by Inna Sysoeva

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
135 KB
Volume
243
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

In 1996, E. Formanek classified all the irreducible complex representations of B n of dimension at most n y 1, where B is the Artin braid group on n strings. In this n paper we extend this classification to the representations of dimension n, for n G 9. We prove that all such representations are equivalent to the tensor product of a one-dimensional representation and a specialization of a certain one-parameter family of n-dimensional representations which was first discovered in 1996 by Tong, Yang, and Ma. In order to do this, we classify all the irreducible complex ลฝ ลฝ . . representations of B for which rank y 1 s 2, where the are the n i i standard generators.

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