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| Fulton W., Pragacz P. — Schubert varieties and degeneracy loci |
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| Предметный указатель |
 -polynomial 91
 -polynomial 83—84 86—91
-polynomial of vector bundle 30 32 82—83 87—90
Addition theorem (linearity formula) 47
Ample divisor 95
Ample vector bundle 97
Arithmetic Schubert calculus 103
Barred permutation 84
Bezout's theorem 1
Bisymmetric polynomial 6
Borel characteristic map 120
Borel — Moore homology 105
Bott — Samelson scheme 112—114
Brill — Noether loci 60—62
Brill — Noether loci in Prym varieties 93—96
Characteristic map 118—122
Chern class 105
Chevalley's formula 122
Class of diagonal 80—82 87 127—128
Complete isotropic flag 65
Complete isotropic flag, standard 65
Complete symmetric polynomial 4 27
Conjugate (or dual) partition 6
Connectedness theorems 97—98
Correspondence 24 114
Cycle classes 104—105
Degree 2
Diagonal embedding 80 127—128
Diagram of permutation 11
Divided difference operator 9—10 43 72—76 85 113—114 136 138
Double Schubert polynomial 9—10 12 15 101—102 110 136 138
Duality formula 6 38
Essential set 11 17
Factorization formula 36—38 44—45
Factorization property for P-polynomials 49
Factorization property for P-polynomials for -polynomials 83
Family, same or opposite, for isotropic subbundles 71 79
Flag variety 20
Gauss — Bonnet formula (or Hopf's theorem) 53
Giambelli formula 18 27 32 70 138
Giambelli — Thom — Porteous formula 15 17 33 38—39 97
Gromov — Witten number 135
Gysin formula or map 17 40—43 45 49—52 81—83 86 88 113—114 119—120 124—126 127—128
Hook length 62
Hook Schur polynomial 5
Hyperoctahedral group 84
Isotropic subspace 29
Jacobi — Trudi ratios or identity 6 34 42
Kempf — Laksov formula 17
Kohnert's conjecture 12—13
Lagrangian Grassmannian 28—29 32—33 80—82 86—87 89
Lagrangian Grassmannian subbundle 71
Lagrangian Grassmannian subspace 29
Laplace-type expansion (for Pfamans) 116
Length of partition 48
Length of permutation 9
| Littlewood — Richardson rule 19 31 47 58 103
Monk's formula 22 103 122
Monomial symmetric polynomial 26
Multi-Schur polynomial 109
Mumford's construction 129—130
Norm (of double unramified cover) 92
P-polynomial of vector bundle 88—89
Parabolic subgroup 121
Partition 5 26
Pfaffian 115—117
Pieri formula 19 27 31 83 103
Poincare duality 104
Polynomial representing degeneracy locus 106—108
Polynomial supported on closed subscheme 108
Polynomial universally supported on degeneracy locus 39 43—45
Polynomial universally supported on degeneracy locus, symmetric or skew- Polynomial universally supported on degeneracy locus, symmetric case 48 50
Positive polynomials 98—99
Prym variety 92—96
Push-forward formula 43 45 124—126
Quantum cohomology 134—138
Quantum cohomology, double Schubert polynomial 136—138
Quantum cohomology, elementary symmetric polynomial 135
Quantum cohomology, Schubert polynomial 135—138
r-general homomorphism 54 56—57 60
Rank conditions 6—9
Reduced decomposition 119
Resultant 46
Schubert cell 19 20 29 66—69 120
Schubert class 19 26 98 120 134
Schubert class, special 27
Schubert polynomials 12—13 21 98—99 103 136—138
Schubert polynomials for classical groups 90—91 101—102
Schubert variety 18 20 26 29 66—69 120
Schur determinant 5—6 15—18 18 27 34 37—39 41—42 45—47 62 70—71 73—76 91 126
Schur P-polynomials 48—50 52 63—64
Schur Pfaffian 29—30 48 83 95
Schur polynomial 5 18—19 34 37 47 50
Schur polynomial in difference of alphabets 37—38 47
Schur polynomial of bundle 38 41—42 45 51 55—56 58 63—64 99—100
Schur polynomial of difference of bundles 38 42—45 51 56—58 124—126
Schur Q-polynomials 31—32 48—52 63—64
Schur — Weyl modules 131—133
Segre classes 28
Special Schubert variety 29
Strict partition 29
Supersymmetric Schur polynomial 5 34—37
Symmetric or skew-symmetric morphism 48—50 63—64 70—71 98
Symmetrizing operator 28 40—42 51—52 85
Symmetrizing operator of Jacobi 41
Symmetrizing operator of Lagrange 40
Tautological bundle 18 27
Tautological bundle, sequence 42
Transverse, intersection of subvarieties 105
Transverse, map to submanifold 53—54 63—64 106
Vexillary permutation 17 109
Whitney formula 105
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