On the Ext Groups between Weyl Modules for Gl N

This paper studies extension groups between certain Weyl modules for the algebraic group GLn 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 between an exterior power of the defining representation and any Weyl module. The significance of these results for modular representation theory of GLn is discussed in several Remarks. Notably the first result leads to a calculation of Ext groups between neighboring Weyl modules for GLn and also recovers the GLn 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.