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Braids,q-Binomials, and Quantum Groups

✍ Scribed by Marcelo Aguiar

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 414 KB
Volume: 20
Category: Article
ISSN: 0196-8858
DOI: 10.1006/aama.1998.0585

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✦ Synopsis

The classical identities between the q-binomial coefficients and factorials can be generalized to a context in which numbers are replaced by braids. More precisely, for every pair i, n of natural numbers, there is defined an element b Ž n. of the braid i group algebra kB , and these satisfy analogs of the classical identities for the n binomial coefficients. By choosing representations of the braid groups, one obtains numerical or matrix realizations of these identities; in particular, one recovers the q-identities in this way. These binomial braids b Ž n. play a crucial role in a simple i q Ž . definition of a family of quantum groups, including the quantum groups U C of q Drinfeld and Jimbo.

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