Abstract
Let \(H = H_q(n)\) be the Hecke algebra of the symmetric group of degree n, over a field of arbitrary characteristic, and where q is a primitive \(\ell \)-th root of unity in K. Let \(H_{\rho }\) be an \(\ell \)-parabolic subalgebra of H. We give an elementary explicit construction for the basic algebra of a non-simple block of \(H_{\rho }\). We also discuss homological properties of \(H_{\rho }\)-modules, in particular existence of varieties for modules, and some consequences.
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Acknowledgements
Most of this material is based on work supported by the National Science Foundation under Grant No. DMS-1440140 while the author was in residence at the Mathematical Sciences Research Institute in Berkeley, California, during part of the Spring 2018 semester. The author thanks Dave Benson and Dan Nakano for discussions related to this material, and thanks to the referee.
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Erdmann, K. On \(\ell \)-parabolic Hecke algebras of symmetric groups. Beitr Algebra Geom 62, 345–362 (2021). https://doi.org/10.1007/s13366-020-00522-7
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DOI: https://doi.org/10.1007/s13366-020-00522-7