Comparing GL n -representations by characteristic-free isomorphisms between generalized Schur algebras

Ming Fang, Anne Henke, Steffen Koenig, Stephen Donkin

Type: Article

Publication Date: 2008-01-01

Citations: 14

DOI: https://doi.org/10.1515/forum.2008.003

Abstract

Isomorphisms 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 ≠ 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. 2000 Mathematics Subject Classification: 16G10, 16W30, 20G05, 20G15.

Locations

arXiv (Cornell University) - PDF
Forum Mathematicum - View

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Works Cited by This (4)

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