On the Ext groups between Weyl modules for GL_n

Details On the Ext groups between Weyl modules for GL_n On the Ext groups between Weyl modules for GL_n

2005-05-18

arxiv.org/abs/math/0505370v1

Mathematics

Representation Theory

plain TeX, 37 pages

Scientific paper

This paper studies extension groups between certain Weyl modules for the algebraic group GL_n over the integers. Main results include: (1) A complete determination of Ext groups between Weyl modules whose highest weights differ by a single root and (2) Determination of Ext^1 between an exterior power of the defining representation and any Weyl module. The significance of these results for modular representation theory of GL_n is discussed in several Remarks. Notably the first result leads to a calculation of Ext groups between neighboring Weyl modules for GL_n and also recovers the GL_n case of a recent result of Andersen. Some generalities about Ext groups between Weyl modules and a brief overview of known results about these groups are also included.

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