Deformed Double Yangian Structures

Details Deformed Double Yangian Structures Deformed Double Yangian Structures

1999-05-18

arxiv.org/abs/math/9905100v1

Rev.Math.Phys. 12 (2000) 945

Mathematics

Quantum Algebra

16 pages, LaTeX2e Document - packages amsfonts,amssymb,subeqnarray

Scientific paper

10.1142/S0129055X00000290

Scaling limits when q tends to 1 of the elliptic vertex algebras A_qp(sl(N)) are defined for any N, extending the previously known case of N=2. They realise deformed, centrally extended double Yangian structures DY_r(sl(N)). As in the quantum affine algebras U_q(sl(N)), and quantum elliptic affine algebras A_qp(sl(N)), these algebras contain subalgebras at critical values of the central charge c=-N-Mr (M integer, 2r=ln p/ln q), which become Abelian when c=-N or 2r=Nh for h integer. Poisson structures and quantum exchange relations are derived for their abstract generators.

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