Abstract
Using results of the author with Cohen and Nakano, we find examples of Young modules for the symmetric group for which the Tate cohomology does not vanish identically, but vanishes for approximately consecutive degrees. We conjecture these vanishing ranges are maximal among all -modules with nonvanishing cohomology. The best known upper bound on such vanishing ranges stands at , due to work of Benson, Carlson and Robinson. Particularly striking, and perhaps counterintuitive, is that these Young modules have maximum possible complexity.
Citation
David Hemmer. "Realizing large gaps in cohomology for symmetric group modules." Algebra Number Theory 6 (4) 825 - 832, 2012. https://doi.org/10.2140/ant.2012.6.825
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