Abstract
We quantize the coordinate ring of the moduli space of B-bundles on the elliptic curve. Here B is a Borel subgroup of some semisimple Lie group. We construct some representations of these algebras and study intertwining operators for these representations. We apply our constructions to produce some objects: the elliptic Belavin R-matrix, the quantization of the algebra of functions on the Grassmannian and some generalized elliptic R-matrix. We consider also the affine case and write down the explicit formula for commuting elements.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Feigin, B.L. and Odesskii, A.V. (1989) Sklyanin’s elliptic algebras, Funkts. Anal. Philozhen. 23, No 3, 45–54.
Feigin, B.L. and Odesskii, A.V. (1993) Constructions of Sklyanin elliptic algebras and quantum.R-matrices”, Funkts. Anal. Philozhen. 27, No 1, 37–45.
Feigin, B.L. and Odesskii, A.V. (1995) Vector Bundles on Elliptic Curve and Sklyanin Algebras, preprint RJMS-1032, Kyoto University, q-alg/9509021.
Cherednik, I.V. (1986) On R-matrix quantization of formal loop groups. Proceedings of the Workshop “Group theoretical methods in physics”, Yurmala, 1985, 2, pp. 161–180, VNU Sci. Press, Utrecht.
Feigin, B.L. and Odesskii, A.V. (1997) A family of elliptic algebras, Internat. Math. Res. Notices, 11, 531–539.
Feigin, B.L. and Odesskii, A.V. (1997) Elliptic deformation of current algebras and their representations by difference operators, Funct. Anal. Appl. 31, No 3, 193–203.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Feigin, B.L., Odesskii, A.V. (2001). Quantized Moduli Spaces of the Bundles on the Elliptic Curve and Their Applications. In: Pakuliak, S., von Gehlen, G. (eds) Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory. NATO Science Series, vol 35. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0670-5_8
Download citation
DOI: https://doi.org/10.1007/978-94-010-0670-5_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-7184-7
Online ISBN: 978-94-010-0670-5
eBook Packages: Springer Book Archive