Pieri resolutions for classical groups

Details Pieri resolutions for classical groups Pieri resolutions for classical groups

2009-07-26

arxiv.org/abs/0907.4505v4

J. Algebra 329 (2011), 222-259

Mathematics

Commutative Algebra

39 pages, no figures; v2: corrections to sections 2.2, 3.1, 3.3, and some typos; v3: important corrections to sections 2.2, 2.

Scientific paper

10.1016/j.jalgebra.2010.03.008

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.

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