Resolution of Weyl modules: the Rota touch
This article is offered as homage to Gian-Carlo Rota. In it, we’ll indicate how the application of Rota’s combinatorial methods to the resolution of Weyl modules changed the way the whole question of finding resolutions was addressed, and what kinds of additional information it led to. To do this, we first have to review briefly the methods that were being used prior to Rota’s involvement. Then we look at how letter-place methods and polarizations provided information that had until his intervention not been forthcoming, such as homotopies and an explicit description of syzygies. Finally, we see how using (generalized) Capelli identities for polarizations leads to a better understanding of the known boundary maps for some resolutions, and provides a direction for finding the general boundary map. We end with a description of the terms of the general resolution of the Weyl module associated to the n-rowed almost skew-shape (see below for definition).
KeywordsDivided Power Place Polarization Koszul Complex General Resolution Weyl Module
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