On commutative algebra and characteristic-free representation theory
type: Item
instance of: scholarly article
title: On commutative algebra and characteristic-free representation theory
zbMATH Open document ID: 0978.13007
DOI: 10.1016/S0022-4049(99)00147-4
author: David A. Buchsbaum
published in: Journal of Pure and Applied Algebra
publication date: 2002-01-18T00:00:00Z
review text: This is a survey, written in an informal style, on the thread holding together commutative algebra, homological algebra, and representation theory. The author discusses ideas and developments in the area of resolutions of determinantal ideals, characteristic free representation theory of the general linear group, Schur and Weyl modules, and their interrelationships.
Mathematics Subject Classification ID: 13C40
Mathematics Subject Classification ID: 13A50
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 20G05
zbMATH DE Number: 1517288
zbMATH Keywords: Koszul complex
zbMATH Keywords: free resolution
zbMATH Keywords: projective resolution
zbMATH Keywords: determinantal ideal
zbMATH Keywords: maximal minors
zbMATH Keywords: Weyl module
zbMATH Keywords: characteristic free representation theory
reviewed by: Matyas Domokos
MaRDI profile type: Publication
cites work: Characteristic-free representation theory of the general linear group
cites work: Characteristic-free representation theory of the general linear group. II: Homological considerations
cites work: Schur functors and Schur complexes
cites work: Resolutions of determinantal ideals: The submaximal minors
cites work: A Generalized Koszul Complex. I
cites work: Some structure theorems for finite free resolutions
cites work: Generic free resolutions and a family of generically perfect ideals
cites work: A Generalized Koszul Complex. II. Depth and Multiplicity
cites work: A Generalized Koszul Complex. III. A Remark on Generic Acyclicity
cites work: Projective resolutions of Weyl modules.
cites work: A new construction in homological algebra.
cites work: On the modular representations of the general linear and symmetric groups
cites work: Invariant theory, Young bitableaux, and combinatorics
cites work: Cohen-Macaulay Rings, Invariant Theory, and the Generic Perfection of Determinantal Loci
cites work: Ideals defined by matrices and a certain complex associated with them
cites work: Multiplicities and equisingularity of ICIS germs
cites work: Q3792822
cites work: Q4295725
cites work: Multiplicities in graded rings II: integral equivalence and the Buchsbaum–Rim multiplicity
cites work: A geometric theory of the Buchsbaum-Rim multiplicity
cites work: Mixed Buchsbaum-Rim Multiplicities
cites work: Syzygies des variétés déterminantales
cites work: Two new functors from modules to algebras
full work available at URL: s0022-4049(99)00147-4
OpenAlex ID: W1997087942
description: scientific article; zbMATH DE number 1517288