Global Weyl modules for the twisted loop algebra

Article

DOI: 10.1007/s12188-013-0074-2

Cite this article as:
Fourier, G., Manning, N. & Senesi, P. Abh. Math. Semin. Univ. Hambg. (2013) 83: 53. 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.

Keywords

Loop algebra Weyl module Symmetric algebra Lie algebra Twisted Kac-Moody algebra 

Mathematics Subject Classification

17B10 17B40 

Copyright information

© Mathematisches Seminar der Universität Hamburg and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Ghislain Fourier
    • 1
  • Nathan Manning
    • 2
  • Prasad Senesi
    • 3
  1. 1.Mathematisches InstitutUniversität zu KölnKölnGermany
  2. 2.University of CaliforniaRiversideUSA
  3. 3.The Catholic University of AmericaWashingtonUSA

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