## On homomorphisms between global Weyl modules

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- by Matthew Bennett, Vyjayanthi Chari, Jacob Greenstein and Nathan Manning
- Represent. Theory
**15**(2011), 733-752 - DOI: https://doi.org/10.1090/S1088-4165-2011-00407-6
- Published electronically: December 20, 2011
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## Abstract:

Let $\mathfrak g$ be a simple finite-dimensional Lie algebra and let $A$ be a commutative associative algebra with unity. Global Weyl modules for the generalized loop algebra $\mathfrak g\otimes A$ were defined by Chari and Pressley (2001) and Feigin and Loktev (2004) for any dominant integral weight $\lambda$ of $\mathfrak g$ 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 $\mathfrak g\otimes A$. 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 $\mathfrak g$, $\lambda$ and $A$. A crucial tool is the construction of fundamental global Weyl modules in terms of fundamental local Weyl modules.## References

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## Bibliographic 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
- 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.)
- © Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Represent. Theory
**15**(2011), 733-752 - MSC (2010): Primary 17B10, 17B37
- DOI: https://doi.org/10.1090/S1088-4165-2011-00407-6
- MathSciNet review: 2869017