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A guide to quantum groups
Introduction 1. Poisson-Lie groups and Lie bialgebras 2. Coboundary Poisson-Lie groups and the classical Yang-Baxter equation 3. Solutions of the classical Yang-Baxter equation 4. QuasitriangularExpand
Elementary Differential Geometry
Curves in the plane and in space.- How much does a curve curve?.- Global properties of curves.- Surfaces in three dimensions.- Examples of surfaces.- The first fundamental form.- Curvature ofExpand
Quantum affine algebras
AbstractWe classify the finite-dimensional irreducible representations of the quantum affine algebra $$U_q (\hat sl_2 )$$ in terms of highest weights (this result has a straightforwardExpand
Weyl modules for classical and quantum affine algebras
We define a family of universal finite-dimensional highest weight modules for affine Lie algebras, we call these Weyl modules. We conjecture that these are the classical limits of the irreducibleExpand
Quantum affine algebras and affine Hecke algebras
One of the most beautiful results from the classical period of the representation theory of Lie groups is the correspondence, due to Frobenius and Schur, between the representations of symmetricExpand
Quantum Affine Algebras at Roots of Unity
We study the restricted form of the qaunatized enveloping algebra of an untwisted affine Lie algebra and prove a triangular decomposition for it. In proving the decomposition we prove several newExpand
An Algebraic Characterization of the Affine Canonical Basis
The canonical basis for quantized universal enveloping algebras associated to the finite--dimensional simple Lie algebras, was introduced by Lusztig. The principal technique is the explicitExpand
Twisted Quantum Affine Algebras
Abstract:We give a highest weight classification of the finite-dimensional irreducible representations of twisted quantum affine algebras. As in the untwisted case, such representations are inExpand