28,442 research outputs found
Conjugacy classes in Weyl groups and q-W algebras
We define noncommutative deformations of algebras of functions on
certain (finite coverings of) transversal slices to the set of conjugacy
classes in an algebraic group which play the role of Slodowy slices in
algebraic group theory. The algebras called q-W algebras are labeled
by (conjugacy classes of) elements of the Weyl group of . The algebra
is a quantization of a Poisson structure defined on the
corresponding transversal slice in with the help of Poisson reduction of a
Poisson bracket associated to a Poisson-Lie group dual to a
quasitriangular Poisson-Lie group. The algebras can be regarded as
quantum group counterparts of W-algebras. However, in general they are not
deformations of the usual W-algebras.Comment: 48 pages; some arguments in the proof of Proposition 12.2 are
clarifie
Geometry of Hyper-K\"ahler Connections with Torsion
The internal space of a N=4 supersymmetric model with Wess-Zumino term has a
connection with totally skew-symmetric torsion and holonomy in \SP(n). We
study the mathematical background of this type of connections. In particular,
we relate it to classical Hermitian geometry construct homogeneous as well as
inhomogeneous examples, characterize it in terms of holomorphic data, develop
its potential theory and reduction theory.Comment: 21 pages, LaTe
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