We compute the braiding for the “principal gradation” of Uq(sl2∧) for |q|=1 from first principles, starting from the idea of a rigid braided tensor category. It is not necessary to assume either the crossing or the unitarity condition from S-matrix theory. We demonstrate the uniqueness of the normalization of the braiding under certain analyticity assumptions, and show that its convergence is critically dependent on the number theoretic properties of the number τ in the deformation parameter q=e2πiτ. We also examine the convergence using probability, assuming a uniform distribution for q on the unit circle.

1.
A. B.
Zamolodchikov
 and
Al. B.
Zamolodchikov
,
Ann. Phys.
120
,
253
(
1979
).
Google Scholar
Crossref
Search ADS
 
2.
R. J. Eden, P. V. Landshoff, D. I. Olive, and J. C. Polkinghorne, The Analytic S-Matrix (Cambridge University Press, Cambridge, 1966).
3.
V. Chari and A. Pressley, A Guide to Quantum Groups (Cambridge University Press, Cambridge, 1994).
4.
S. Majid, Foundations of Quantum Group Theory (Cambridge University Press, Cambridge, 1995).
5.
P. R.
Johnson
,
Nucl. Phys. B
496
,
505
(
1997
).
Google Scholar
Crossref
Search ADS
 
6.
E. J.
Beggs
and
P. R.
Johnson
,
Nucl. Phys. B
484
,
653
(
1997
).
Google Scholar
Crossref
Search ADS
 
7.
D.
Bernard
and
A.
Leclair
,
Commun. Math. Phys.
142
,
99
(
1991
).
Google Scholar
Crossref
Search ADS
 
8.
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th. ed. (Oxford University Press, Oxford, 1979).
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© 2001 American Institute of Physics.
2001
American Institute of Physics
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