Pieri resolutions for classical groups
Abstract
We generalize the constructions of Eisenbud, Fl{\o}ystad, and Weyman for equivariant minimal free resolutions over the general linear group, and we construct equivariant resolutions over the orthogonal and symplectic groups. We also conjecture and provide some partial results for the existence of an equivariant analogue of Boij-S\"oderberg decompositions for Betti tables, which were proven to exist in the non-equivariant setting by Eisenbud and Schreyer. Many examples are given.
Cite
@article{arxiv.0907.4505,
title = {Pieri resolutions for classical groups},
author = {Steven V Sam and Jerzy Weyman},
journal= {arXiv preprint arXiv:0907.4505},
year = {2012}
}
Comments
40 pages, no figures; v2: corrections to sections 2.2, 3.1, 3.3, and some typos; v3: important corrections to sections 2.2, 2.3 and Prop. 4.9 added, plus other minor corrections; v4: added assumptions to Theorem 3.6 and updated its proof; v5: Older versions misrepresented Peter Olver's results. See "New in this version" at the end of the introduction for more details