Quantization of Lie bialgebras, IV
| dc.creator | Etingof, Pavel | |
| dc.creator | Kazhdan, David | |
| dc.date | 1998-01-09 | |
| dc.date | 1998-08-28 | |
| dc.date.accessioned | 2026-07-07T05:23:33Z | |
| dc.date.available | 2026-07-07T05:23:33Z | |
| dc.description | This paper is a continuation of "Quantization of Lie bialgebras, III" (q-alg/9610030, revised version). In QLB-III, we introduced the Hopf algebra F(R)_\z associated to a quantum R-matrix R(z) with a spectral parameter, and a set of points \z=(z_1,...,z_n). This algebra is generated by entries of a matrix power series T_i(u), i=1,...,n,subject to Faddeev-Reshetikhin-Takhtajan type commutation relations, and is a quantization of the group GL_N[[t]]. In this paper we consider the quotient F_0(R)_\z of F(R)_\z by the relations \qdet_R(T_i)=1, where \qdet_R is the quantum determinant associated to R (for rational, trigonometric, or elliptic R-matrices). This is also a Hopf algebra, which is a quantization of the group SL_N[[t]]. This paper was inspired by the pioneering paper of I.Frenkel and Reshetikhin. The main goal of this paper is to study the representation theory of the algebra F_0(R)_\z and of its quantum double, and show how the consideration of coinvariants of this double (quantum conformal blocks) naturally leads to the quantum Knizhnik-Zamolodchikov equations of Frenkel and Reshetikhin. Our construction for the rational R-matrix is a quantum analogue of the standard derivation of the Knizhnik-Zamolodchikov equations in the Wess-Zumino-Witten model of conformal field theory, and for the elliptic R-matrix is a quantum analogue of the construction of Kuroki and Takebe. Our result is a generalization of the construction of Enriques and Felder, which appeared while this paper was in preparation. Enriques and Felder gave a derivation of the quantum KZ equations from coinvariants in the case of the rational R-matrix and N=2. | |
| dc.description | 22 pages, amstex. This is the 4-th part of the Quantization series, starting from q-alg/9506005; in the revised version, some errors in formulas in Chapter 5 have been corrected | |
| dc.identifier | https://arxiv.org/abs/math/9801043 | |
| dc.identifier | http://arxiv.org/abs/math/9801043 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76479 | |
| dc.subject | Quantum Algebra | |
| dc.title | Quantization of Lie bialgebras, IV | |
| dc.type | text |