|
SIGMA 5 (2009), 006, 4 pages arXiv:0901.2335
https://doi.org/10.3842/SIGMA.2009.006
Contribution to the Proceedings of the XVIIth International Colloquium on Integrable Systems and Quantum Symmetries
Heisenberg-Type Families in Uq(^sl2)
Alexander Zuevsky
Max-Planck Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
Received October 20, 2008, in final form January 13, 2009; Published online January 15, 2009
Abstract
Using the second Drinfeld formulation of the quantized universal enveloping algebra
Uq(^sl2) we introduce a family of its Heisenberg-type elements which are endowed with a
deformed commutator and satisfy properties similar to
generators of a Heisenberg subalgebra.
Explicit expressions for new family of generators are found.
Key words:
quantized universal enveloping algebras; Heisenberg-type families.
pdf (171 kb)
ps (126 kb)
tex (8 kb)
References
- Drinfel'd V.G., A new realization of Yangians and quantized
affine algebras, Soviet Math. Dokl. 36 (1988), 212-216.
- Enriquez B., Quantum principal commutative subalgebra in the nilpotent part of
Uqsl2 and lattice KdV variables, Comm. Math. Phys. 170
(1995), 197-206, hep-th/9402145.
- Frenkel I.B., Jing N.H., Vertex representations of quantum
affine algebras, Proc. Nat. Acad. Sci. USA 85 (1988), 9373-9377.
- Jimbo M., Miki K., Miwa T., Nakayashiki A.,
Correlation functions of the XXZ model for D < -1,
Phys. Let. A 168 (1992), 256-263, hep-th/9205055.
- Kac V.G., Infinite-dimensional Lie algebras, 3rd ed.,
Cambridge University Press, Cambridge, 1990.
- Saveliev M.V., Zuevsky A.B., Quantum vertex
operators for the sine-Gordon model,
Internat. J. Modern Phys. A 15 (2000),
3877-3897.
- Zuevsky A., Heisenberg-type families of
Uq(^G), in preparation.
|
|