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Demazure modules and Weyl modules: The twisted current case


Authors: Ghislain Fourier and Deniz Kus
Journal: Trans. Amer. Math. Soc. 365 (2013), 6037-6064
MSC (2010): Primary 17B10; Secondary 17B65
DOI: https://doi.org/10.1090/S0002-9947-2013-05846-1
Published electronically: June 13, 2013
MathSciNet review: 3091275
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Abstract: We study finite-dimensional respresentations of twisted current algebras and show that any graded twisted Weyl module is isomorphic to level one Demazure modules for the twisted affine Kac-Moody algebra. Using the tensor product property of Demazure modules, we obtain, by analyzing the fundamental Weyl modules, dimension and character formulas. Moreover, we prove that graded twisted Weyl modules can be obtained by taking the associated graded modules of Weyl modules for the loop algebra, which implies that its dimension and classical character are independent of the support and depend only on its classical highest weight. These results were previously known for untwisted current algebras and are new for all twisted types.


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Additional Information

Ghislain Fourier
Affiliation: Mathematisches Institut, Universität zu Köln, 50931 Köln, Germany
Email: gfourier@math.uni-koeln.de

Deniz Kus
Affiliation: Mathematisches Institut, Universität zu Köln, 50931 Köln, Germany
Email: dkus@math.uni-koeln.de

DOI: https://doi.org/10.1090/S0002-9947-2013-05846-1
Received by editor(s): September 12, 2011
Received by editor(s) in revised form: March 30, 2012
Published electronically: June 13, 2013
Article copyright: © Copyright 2013 American Mathematical Society

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