Extensions of Modules over Schur Algebras, Symmetric Groups and Hecke Algebras |
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Authors: | Stephen R. Doty Karin Erdmann Daniel K. Nakano |
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Affiliation: | (1) Mathematical and Computer Sciences, Loyola University Chicago, Chicago, IL, 60626, U.S.A.;(2) Mathematical Institute, Oxford University, 24-29 St, Giles, Oxford, OX1 3LB, England;(3) Department of Mathematics, University of Georgia, Athens, GA, 30602, U.S.A. |
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Abstract: | We study the relation between the cohomology of general linear and symmetric groups and their respective quantizations, using Schur algebras and standard homological techniques to build appropriate spectral sequences. As our methods fit inside a much more general context within the theory of finite-dimensional algebras, we develop our results first in that general setting, and then specialize to the above situations. From this we obtain new proofs of several known results in modular representation theory of symmetric groups. Moreover, we reduce certain questions about computing extensions for symmetric groups and Hecke algebras to questions about extensions for general linear groups and their quantizations. |
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Keywords: | Schur algebras Hecke algebras extensions cohomology finite-dimensional algebra |
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