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Semisimple Schur Algebras

Published online by Cambridge University Press:  01 July 1998

STEPHEN R. DOTY  and
DANIEL K. NAKANO
STEPHEN R. DOTY
Affiliation:
Mathematical Sciences, Loyola University Chicago, Chicago, Illinois 60626 U.S.A. e-mail: doty@math.luc.edu
DANIEL K. NAKANO
Affiliation:
Mathematical Sciences, Loyola University Chicago, Chicago, Illinois 60626 U.S.A. e-mail: doty@math.luc.edu
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Abstract

Schur algebras are certain finite-dimensional algebras that completely control the polynomial representation theory of the general linear groups over an infinite field. Infinitesimal Schur algebras are truncated versions of the classical Schur algebras which control the polynomial representation theory of the Frobenius kernels of general linear groups. In this paper we use some elementary results on symmetric powers to classify the semisimple Schur algebras. We then classify the semisimple infinitesimal Schur algebras as well.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 124 , Issue 1 , July 1998 , pp. 15 - 20
Copyright
Cambridge Philosophical Society 1998

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