Skew Weyl Modules for GLn and Degree Reduction for Schur Algebras

✍ Scribed by Upendra Kulkarni

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 103 KB
• Volume: 224
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1999.8042

✦ Synopsis

We prove a strong characteristic-free analogue of the classical adjoint formula s λ s µ f = s λ/µ f in the ring of symmetric functions. This is done by showing that the representative of a suitably chosen functor involving a tensor product is the skew Weyl module. By "strong" we mean that this representative preserves not only Hom groups, but higher Ext groups also-a fact which can be used to compute some homological invariants of Weyl modules for GL n via recursion on degree. We use the following main tools: existence of Weyl filtrations in tensor products of Weyl modules, the Akin-Buchsbaum-Weyman constructions of Weyl modules and certain vanishing properties of Ext groups.