On homomorphisms between global Weyl modules

Author:

Bennett Matthew,Chari Vyjayanthi,Greenstein Jacob,Manning Nathan

Abstract

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

Publisher

American Mathematical Society (AMS)

Subject

Mathematics (miscellaneous)

Reference11 articles.

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4. Weyl, Demazure and fusion modules for the current algebra of 𝔰𝔩ᵣ₊₁;Chari, Vyjayanthi;Adv. Math.,2006

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