Global Weyl modules for the twisted loop algebra

Fourier, G., Manning, N. and Senesi, P. (2013) Global Weyl modules for the twisted loop algebra. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 83(1), pp. 53-82. (doi: 10.1007/s12188-013-0074-2)

Abstract

We define global Weyl modules for twisted loop algebras and analyze their highest 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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Fourier, Dr Ghislain
• Authors: Fourier, G., Manning, N., and Senesi, P.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
• Publisher: Springer Verlag
• ISSN: 0025-5858
• ISSN (Online): 1865-8784