Deformed Double Yangian Structures
Abstract
Scaling limits when q tends to 1 of the elliptic vertex algebras Aqp(sl(N)) are defined for any N, extending the previously known case of N=2. They realise deformed, centrally extended double Yangian structures DYr(sl(N)). As in the quantum affine algebras Uq(sl(N)), and quantum elliptic affine algebras Aqp(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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