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On commutative algebra and characteristic-free representation theory. (English) Zbl 0978.13007

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.

MSC:

13C40 Linkage, complete intersections and determinantal ideals
13A50 Actions of groups on commutative rings; invariant theory
13A15 Ideals and multiplicative ideal theory in commutative rings
20G05 Representation theory for linear algebraic groups
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