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| Recollections and Perspectives | |
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| Factorization | |
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| Factorization domains | |
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| Polynomial and power series rings | |
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| Linear algebra | |
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| Free modules | |
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| Projective modules | |
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| Projective resolutions | |
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| Multilinear algebra | |
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| R[X[subscript 1],..., X[subscript t]] as a symmetric algebra | |
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| The divided power algebra | |
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| The exterior algebra | |
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| Local Ring Theory | |
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| Koszul complexes | |
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| Local rings | |
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| Hilbert-Samuel polynomials | |
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| Codimension and finitistic global dimension | |
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| Regular local rings | |
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| Unique factorization | |
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| Multiplicity | |
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| Intersection multiplicity and the homological conjectures | |
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| Generalized Koszul Complexes | |
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| A few standard complexes | |
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| The graded Koszul complex and its "derivatives" | |
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| Definitions of the hooks and their explicit bases | |
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| General setup | |
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| The fat complexes | |
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| Slimming down | |
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| Families of complexes | |
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| The "homothety homotopy" | |
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| Comparison of the fat and slim complexes | |
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| Depth-sensitivity of T(q; f) | |
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| Another kind of multiplicity | |
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| Structure Theorems for Finite Free Resolutions | |
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| Some criteria for exactness | |
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| The first structure theorem | |
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| Proof of the first structure theorem | |
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| Part (a) | |
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| Part (b) | |
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| The second structure theorem | |
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| Exactness Criteria at Work | |
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| Pfaffian ideals | |
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| Pfaffians | |
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| Resolution of a certain pfaffian ideal | |
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| Algebra structures on resolutions | |
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| Proof of Part 2 of Theorem V.1.8 | |
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| Powers of pfaffian ideals | |
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| Intrinsic description of the matrix X | |
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| Hooks again | |
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| Some representation theory | |
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| A counting argument | |
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| Description of the resolutions | |
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| Proof of Theorem V.2.4 | |
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| Weyl and Schur Modules | |
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| Shape matrices and tableaux | |
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| Shape matrices | |
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| Tableaux | |
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| Weyl and Schur modules associated to shape matrices | |
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| Letter-place algebra | |
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| Positive places and the divided power algebra | |
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| Negative places and the exterior algebra | |
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| The symmetric algebra (or negative letters and places) | |
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| Putting it all together | |
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| Place polarization maps and Capelli identities | |
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| Weyl and Schur maps revisited | |
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| Some kernel elements of Weyl and Schur maps | |
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| Tableaux, straightening, and the straight basis theorem | |
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| Tableaux for Weyl and Schur modules | |
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| Straightening tableaux | |
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| Taylor-made tableaux, or a straight-filling algorithm | |
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| Proof of linear independence of straight tableaux | |
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| Modifications for Schur modules | |
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| Duality | |
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| Weyl-Schur complexes | |
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| Some Applications of Weyl and Schur Modules | |
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| The fundamental exact sequence | |
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| Direct sums and filtrations for skew-shapes | |
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| Resolution of determinantal ideals | |
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| The Lascoux resolutions | |
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| The submaximal minors | |
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| Z-forms | |
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| Arithmetic considerations | |
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| Intertwining numbers | |
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| Z-forms again | |
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| Resolutions revisited; the Hashimoto counterexample | |
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| Resolutions of Weyl modules | |
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| The bar complex | |
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| The two-rowed case | |
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| A three-rowed example | |
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| Resolutions of skew-hooks | |
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| Comparison with the Lascoux resolutions | |
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| Appendix for Letter-Place Methods | |
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| Theorem VI.3.2, Part 1: the double standard tableaux generate | |
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| Theorem VI.3.2 Part 2: linear independence of double standard tableaux | |
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| Modifications required for Theorems VI.3.3 and VI.3.4 | |
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| Modifications required for Theorem VI.8.4 | |
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| References | |
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| Index | |