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Journal of Lie Theory 24 (2014), No. 2, 503--527
Copyright Heldermann Verlag 2014

Weyl Modules and Levi Subalgebras

Ghislain Fourier
Mathematisches Institut, Universität Köln, Weyertal 86-90, 50931 Köln, Germany

For a simple complex Lie algebra g of classical type we are studying the restriction of modules of the current algebra to the current algebra of a Levi subalgebra of g. More precisely, we are studying the highest weight components of simple modules, global and local Weyl modules. We are identifying necessary and sufficient conditions on a pair of a Levi subalgebra and a dominant integral weight, such that the highest weight component of the restricted module is a global (resp., a local) Weyl module.

Keywords: Weyl modules, Levi subalgebra, Current algebra.

MSC: 17B10, 17B67

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