65 research outputs found
Area-Preserving Algebra Structure of Two-Dimensional Supergravity
The effective action for 2d-gravity in Weyl-invariant regularization is
extended to supersymmetric case. The super area-preserving invariance and
cocyclic properties under general supergravitational transformations of the
last action is shown.Comment: latex file, no figures, 5 pages. Some references are adde
Orthogonal and symplectic Yangians and Yang-Baxter R-operators
Yang-Baxter R operators symmetric with respect to the orthogonal and
symplectic algebras are considered in an uniform way. Explicit forms for the
spinorial and metaplectic R operators are obtained. L operators, obeying the
RLL relation with the orthogonal or symplectic fundamental R matrix, are
considered in the interesting cases, where their expansion in inverse powers of
the spectral parameter is truncated. Unlike the case of special linear algebra
symmetry the truncation results in additional conditions on the Lie algebra
generators of which the L operators is built and which can be fulfilled in
distinguished representations only. Further, generalised L operators, obeying
the modified RLL relation with the fundamental R matrix replaced by the
spinorial or metaplectic one, are considered in the particular case of linear
dependence on the spectral parameter. It is shown how by fusion with respect to
the spinorial or metaplectic representation these first order spinorial L
operators reproduce the ordinary L operators with second order truncation.Comment: 24 page
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