Comparing $GL_n$-Representations by Characteristic-Free Isomorphisms between Generalized Schur Algebras

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dc.creatorFang, Ming
dc.creatorHenke, Anne
dc.creatorKoenig, Steffen
dc.date2007-08-29
dc.date.accessioned2026-07-07T08:26:35Z
dc.date.available2026-07-07T08:26:35Z
dc.descriptionIsomorphisms are constructed between generalized Schur algebras in different degrees. The construction covers both the classical case (of general linear groups over infinite fields of arbitrary characteristic) and the quantized case (in type $A$, for any non-zero value of the quantum parameter $q$). The construction does not depend on the characteristic of the underlying field or the choice of $q \neq 0$. The proof combines a combinatorial construction with comodule structures and Ringel duality. Applications range from equivalences of categories to results on the structure and cohomology of Schur algebras to identities of decomposition numbers and also of $p$-Kostka numbers, in both cases reproving and generalizing row and column removal rules.
dc.identifierhttps://arxiv.org/abs/0708.4019
dc.identifierhttp://arxiv.org/abs/0708.4019
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/136990
dc.subjectRepresentation Theory
dc.subject20G05
dc.titleComparing $GL_n$-Representations by Characteristic-Free Isomorphisms between Generalized Schur Algebras
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