University of California Riverside Global Weyl Modules for Twisted and Untwisted Loop Algebras Abstract of the Dissertation Global Weyl Modules for Twisted and Untwisted Loop Algebras

OF THE DISSERTATION Global Weyl Modules for Twisted and Untwisted Loop Algebras by Nathaniael Jared Manning Doctor of Philosophy, Graduate Program in Mathematics University of California, Riverside, June 2012 Dr. Vyjayanthi Chari, Chairperson A family of modules called global Weyl modules were defined in [7] over algebras of the form g⊗A, where g is a simple finite–dimensional complex Lie algebra and A is a commutative associative algebra with unity. Part I of this dissertation contains a characterization the homomorphisms between these global Weyl modules, under certain restrictions on g and A. The crucial tool in this section is the reconstruction of the fundamental global Weyl module from a local one. In Part II, global Weyl modules are defined for the first time for loop algebras which have been twisted by a graph automorphism of the Dynkin diagram. We analyze their relationship with the twisted local Weyl module, which was defined in [8], and with the untwisted global Weyl module.