The image of the Specht module under the inverse Schur functor in arbitrary characteristic. / McDowell, Eoghan.

In: Journal of Algebra, Vol. 586, 15.11.2021, p. 865-898.

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Abstract

This paper gives a necessary and sufficient condition for the image of the Specht module under the inverse Schur functor to be isomorphic to the dual Weyl module in characteristic 2, and gives an elementary proof that this isomorphism holds in all cases in all other characteristics. These results are new in characteristics 2 and 3. We deduce some new examples of indecomposable Specht modules in characteristic 2. When the isomorphism does not hold, the dual Weyl module is still a quotient of the image of the Specht module, and we prove some additional results: we demonstrate that the image need not have a filtration by dual Weyl modules, we bound the dimension of the kernel of the quotient map, and we give some explicit descriptions for particular cases. Our method is to view the Specht and dual Weyl modules as quotients of suitable exterior powers by the Garnir relations.
Original languageEnglish
Pages (from-to)865-898
Number of pages34
JournalJournal of Algebra
Volume586
Early online date29 Jul 2021
DOIs
Publication statusE-pub ahead of print - 29 Jul 2021
This open access research output is licenced under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

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