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Harish-Chandra Vertices and Steinberg's Tensor Product Theorems for Finite General Linear Groups |
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| Authors: | Dipper, R Du, J |
| Affiliation: | Mathematische Institut B, Universität Stuttgart 70550 Stuttgart, Germany. E-mail: rdipper{at}methematik.uni-stuttgart.de School of Mathematics, University of New South Wales Sydney 2052, Australia. E-mail: j.du{at}unsw.edu.au and jied{at}alpha.maths.unsw.edu.au |
| Abstract: | Representations of Hecke and q-Schur algebras are closely relatedto those of finite general linear groups G in non-describingcharacteristics. Such a relationship can be described by certainfunctors. Using these functors, we determine the Harish-Chandravertices and sources of certain indecomposable G-modules. TheGreen correspondence is investigated in this context. As a furtherapplication of our theory, we establish Steinberg's tensor producttheorems for irreducible representations of G in non-describingcharacteristics. 1991 Mathematics Subject Classification: 20C20,20C33, 20G05, 20G40. |
| Keywords: | Harish-Chandra vertex tensor product theorem Hecke algebra q-Schur algebra finite general linear group |
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