Deformed Double Yangian Structures

D. Arnaudon; J. Avan; L. Frappat; M. Rossi

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arxiv math/9905100 v1 pith:G4M3VH5P submitted 1999-05-18 math.QA math-phmath.MP

Deformed Double Yangian Structures

D. Arnaudon , J. Avan , L. Frappat , M. Rossi This is my paper

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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.

Deformed Double Yangian Structures

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