On homomorphisms between global Weyl modules

Authors:
Matthew Bennett, Vyjayanthi Chari, Jacob Greenstein and Nathan Manning

Journal:
Represent. Theory **15** (2011), 733-752

MSC (2010):
Primary 17B10, 17B37

DOI:
https://doi.org/10.1090/S1088-4165-2011-00407-6

Published electronically:
December 20, 2011

MathSciNet review:
2869017

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a simple finite-dimensional 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 one-dimensional and also that any non-zero 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:
https://doi.org/10.1090/S1088-4165-2011-00407-6

Received by editor(s):
December 2, 2010

Received by editor(s) in revised form:
March 9, 2011

Published electronically:
December 20, 2011

Additional Notes:
The second and third authors were partially supported by DMS-0901253 (V.C.) and DMS-0654421 (J.G.)

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.