On homomorphisms between global Weyl modules
Authors:
Matthew Bennett, Vyjayanthi Chari, Jacob Greenstein and Nathan Manning
Journal:
Represent. Theory 15 (2011), 733752
MSC (2010):
Primary 17B10, 17B37
Posted:
December 20, 2011
MathSciNet review:
2869017
Fulltext PDF Free Access
Abstract 
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Abstract: Let be a simple finitedimensional Lie algebra and let be a commutative associative algebra with unity. Global Weyl modules for the generalized loop algebra were defined by Chari and Pressley (2001) and Feigin and Loktev (2004) for any dominant integral weight of by generators and relations and further studied by Chari, Fourier, and Khandai (2010). They are expected to play a role similar to that of Verma modules in the study of categories of representations of . One of the fundamental properties of Verma modules is that the space of morphisms between two Verma modules is either zero or onedimensional and also that any nonzero morphism is injective. The aim of this paper is to establish an analogue of this property for global Weyl modules. This is done under certain restrictions on , and . A crucial tool is the construction of fundamental global Weyl modules in terms of fundamental local Weyl modules.
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Additional Information
Matthew Bennett
Affiliation:
Department of Mathematics, University of California, Riverside, California 92521
Email:
mbenn002@math.ucr.edu
Vyjayanthi Chari
Affiliation:
Department of Mathematics, University of California, Riverside, California 92521
Email:
vyjayanthi.chari@ucr.edu
Jacob Greenstein
Affiliation:
Department of Mathematics, University of California, Riverside, California 92521
Email:
jacob.greenstein@ucr.edu
Nathan Manning
Affiliation:
Department of Mathematics, University of California, Riverside, California 92521
Email:
nmanning@math.ucr.edu
DOI:
http://dx.doi.org/10.1090/S108841652011004076
PII:
S 10884165(2011)004076
Received by editor(s):
December 2, 2010
Received by editor(s) in revised form:
March 9, 2011
Posted:
December 20, 2011
Additional Notes:
The second and third authors were partially supported by DMS0901253 (V.C.) and DMS0654421 (J.G.)
Article copyright:
© Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
