Differential-difference system related to toroidal Lie algebra
نویسندگان
چکیده
We present a novel differential-difference system in (2+1)-dimensional space-time (one discrete, two continuum), arisen from the Bogoyavlensky’s (2+1)-dimensional KdV hierarchy. Our method is based on the bilinear identity of the hierarchy, which is related to the vertex operator representation of the toroidal Lie algebra sl 2 .
منابع مشابه
Modules of the toroidal Lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$
Highest weight modules of the double affine Lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$ are studied under a new triangular decomposition. Singular vectors of Verma modules are determined using a similar condition with horizontal affine Lie subalgebras, and highest weight modules are described under the condition $c_1>0$ and $c_2=0$.
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