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J. A. Green (1980)
GLn Polynomial Representations of
K. Akin, D. A. Buchsbaum, J. Weyman (1982)
Schur functors and Schur compolexesAdv. in Math., 44
V. Lakshmibai, C. Musili, C. S. Seshadri (1974)
Cohomology of line bundles on G/BAnn. Sci. École Norm. Sup., 7
K. Akin, D. A. Buchsbaum (1988)
Characteristic-free representation theory of the general linear group, II: Homological considerationsAdv. in Math., 72
J. Towber (1977)
Two new functors from modules to algebrasJ. Algebra, 47
R. W. Carter, G. Lusztig (1974)
On the modular representations of the general linear and symmetric groupsMath. Z., 136
K. Akin, D. A. Buchsbaum (1985)
Characteristics-free representation theory of the general linear groupAdv. in Math., 58
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
Acta Applicandae Mathematicae – Springer Journals
Published: May 7, 2004
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