Low-dimensional unitary representations of

Author:
Imre Tuba

Journal:
Proc. Amer. Math. Soc. **129** (2001), 2597-2606

MSC (1991):
Primary 20F36, 20C07, 81R10; Secondary 20H20, 16S34

DOI:
https://doi.org/10.1090/S0002-9939-01-05903-2

Published electronically:
March 15, 2001

MathSciNet review:
1838782

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Abstract | References | Similar Articles | Additional Information

We characterize all simple unitarizable representations of the braid group on complex vector spaces of dimension . In particular, we prove that if and denote the two generating twists of , then a simple representation (for ) is unitarizable if and only if the eigenvalues of are distinct, satisfy and for , where the are functions of the eigenvalues, explicitly described in this paper.

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Additional Information

**Imre Tuba**

Affiliation:
Department of Mathematics, Mail Code 0112, University of California, San Diego, 9500 Gilman Dr., La Jolla, California 92093-0112

Address at time of publication:
Department of Mathematics, University of California, Santa Barbara, California 93106

Email:
ituba@math.ucsd.edu, ituba@math.ucsb.edu

DOI:
https://doi.org/10.1090/S0002-9939-01-05903-2

Received by editor(s):
August 31, 1999

Received by editor(s) in revised form:
January 31, 2000

Published electronically:
March 15, 2001

Communicated by:
Stephen D. Smith

Article copyright:
© Copyright 2001
American Mathematical Society