ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

11. Mathematical Physics

1991 MS Classification: 20, 81, 82 Konno, Hitoshi, Hiroshima University Elliptic quantum groups. We will present two types of quasi-Hopf algebras A_{q,p}(𝔰̂𝔩_{n}) and B_{q,λ}(𝔤) (𝔤 being Kac-Moody algebra with symmetrizable GCM), which are elliptic deformations of the quantum group U_{q}(𝔤) (𝔤 = 𝔰̂𝔩_{n} for the former)[1], corresponding to two types of exactly solvable lattice models, the vertex type and the face type. In addition, defining the algebra U_{q,p}(𝔤) (𝔤 being untwisted affine Lie algebra) as a tensor product of B_{q,λ}(𝔤) and one Heisenberg algebra, we will present its relation to the q-deformation of the W -algebra associated with 𝔤[1,2]. Reference:

[1] M. Jimbo, H. Konno, S. Odake and J. Shiraishi, Quasi-Hopf twistors for elliptic quantum groups, q-alg/9712029, to appear in Transform. Groups; Elliptic algebra U_{q,p}(𝔰̂𝔩_{2}): Drinfeld current and vertex operators, qalg/9802002.

[2] H. Konno, An elliptic algebra U_{q,p}(𝔰̂𝔩_{2}) and the fusion RSOS model, q-alg/9709013, to appear in Comm. Math. Phys.