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Aspects of characteristic-free representation theory of GLn, and some applications to intertwining numbers

Aspects of characteristic-free representation theory of GLn, and some applications to... Acta Applicandae Mathematicae 21: 247-261, 1990. © 1990 Kluwer Academic Publishers. Printed in the Netherlands. Aspects of characteristic-free representation theory of GLn, and some applications to intertvining numbers. by David A. Buchsbaum Department of Mathematics, Brandeis University, Waltham, MA 02154, U.S.A. §2. Introdsction Characteristic-free representation theory has been studied by many people over the past fifteen years in many different ways for many different reasons. In the mid-seventies, Carter and Lusztig [6] defined the Weyl modules for the general linear group over any field, indepen- dent of characteristic. Towber, a little later [9], defined the Schur and Yeyl modules for GL n over an arbitrary commutative ring. Using standard monomial theory, Lakshmibai, Musili and Seshadri [8] defined the Schur modules for the classical groups over any commutative ring. For the kinds of problems that grew out of the study of resolu- tions of determinantal ideals, it was necessary not only to reproduce the Schur and ~eyl modules over an arbitrary commutative ring, but to have a larger category of representations to hand in order to use exact sequences, spectral sequences and other homological tools. In large part, the use of homological methods compensates for the inapplicability to a characteristic-free http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Aspects of characteristic-free representation theory of GLn, and some applications to intertwining numbers

Acta Applicandae Mathematicae , Volume 21 (2) – May 7, 2004

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References (7)

Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/BF00053299
Publisher site
See Article on Publisher Site

Abstract

Acta Applicandae Mathematicae 21: 247-261, 1990. © 1990 Kluwer Academic Publishers. Printed in the Netherlands. Aspects of characteristic-free representation theory of GLn, and some applications to intertvining numbers. by David A. Buchsbaum Department of Mathematics, Brandeis University, Waltham, MA 02154, U.S.A. §2. Introdsction Characteristic-free representation theory has been studied by many people over the past fifteen years in many different ways for many different reasons. In the mid-seventies, Carter and Lusztig [6] defined the Weyl modules for the general linear group over any field, indepen- dent of characteristic. Towber, a little later [9], defined the Schur and Yeyl modules for GL n over an arbitrary commutative ring. Using standard monomial theory, Lakshmibai, Musili and Seshadri [8] defined the Schur modules for the classical groups over any commutative ring. For the kinds of problems that grew out of the study of resolu- tions of determinantal ideals, it was necessary not only to reproduce the Schur and ~eyl modules over an arbitrary commutative ring, but to have a larger category of representations to hand in order to use exact sequences, spectral sequences and other homological tools. In large part, the use of homological methods compensates for the inapplicability to a characteristic-free

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: May 7, 2004

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