Global Weyl modules for the twisted loop algebra

Details Global Weyl modules for the twisted loop algebra Global Weyl modules for the twisted loop algebra

2011-10-12

arxiv.org/abs/1110.2752v2

Mathematics

Representation Theory

30 pages. Bibliography updated, typographical errors fixed

Scientific paper

We define global Weyl modules for twisted loop algebras and analyze their high- est weight spaces, which are in fact isomorphic to Laurent polynomial rings in finitely many variables. We are able to show that the global Weyl module is a free module of finite rank over these rings. Furthermore we prove, that there exist injective maps from the global Weyl modules for twisted loop algebras into a direct sum of global Weyl modules for untwisted loop algebras. Relations between local Weyl modules for twisted and untwisted generalized current algebras are known; we provide for the first time a relation on global Weyl modules.

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