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Geometry of G/P. (English) Zbl 0466.14020

MSC:
14M15 Grassmannians, Schubert varieties, flag manifolds
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
20G15 Linear algebraic groups over arbitrary fields
14L35 Classical groups (algebro-geometric aspects)
14L30 Group actions on varieties or schemes (quotients)
14L24 Geometric invariant theory
14M17 Homogeneous spaces and generalizations
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[1] Michel Demazure, Désingularisation des variétés de Schubert généralisées, Ann. Sci. École Norm. Sup. (4) 7 (1974), 53 – 88 (French). Collection of articles dedicated to Henri Cartan on the occasion of his 70th birthday, I. · Zbl 0312.14009
[2] W. V. D. Hodge, Some enumerative results in the theory of forms, Proc. Cambridge Philos. Soc. 39 (1943), 22 – 30. · Zbl 0060.04107
[3] George R. Kempf, Linear systems on homogeneous spaces, Ann. of Math. (2) 103 (1976), no. 3, 557 – 591. · Zbl 0327.14016 · doi:10.2307/1970952 · doi.org
[4] C. S. Seshadri, Geometry of \?/\?. I. Theory of standard monomials for minuscule representations, C. P. Ramanujam — a tribute, Tata Inst. Fund. Res. Studies in Math., vol. 8, Springer, Berlin-New York, 1978, pp. 207 – 239. V. Lakshmibai and C. S. Seshadri, Geometry of \?/\?. II. The work of de Concini and Procesi and the basic conjectures, Proc. Indian Acad. Sci. Sect. A 87 (1978), no. 2, 1 – 54. V. Lakshmibai, C. Musili, and C. S. Seshadri, Geometry of \?/\?. III. Standard monomial theory for a quasi-minuscule \?, Proc. Indian Acad. Sci. Sect. A Math. Sci. 88 (1979), no. 3, 93 – 177. V. Lakshmibai, C. Musili, and C. S. Seshadri, Geometry of \?/\?. IV. Standard monomial theory for classical types, Proc. Indian Acad. Sci. Sect. A Math. Sci. 88 (1979), no. 4, 279 – 362. · Zbl 0447.14011
[5] V. Lakshmibai, Geometry of G/P-IV (Standard monomial theory for classical types), Proc. Indian Acad. Sci. (to appear). · Zbl 0447.14013
[6] C. S. Seshadri, Geometry of \?/\?. I. Theory of standard monomials for minuscule representations, C. P. Ramanujam — a tribute, Tata Inst. Fund. Res. Studies in Math., vol. 8, Springer, Berlin-New York, 1978, pp. 207 – 239. V. Lakshmibai and C. S. Seshadri, Geometry of \?/\?. II. The work of de Concini and Procesi and the basic conjectures, Proc. Indian Acad. Sci. Sect. A 87 (1978), no. 2, 1 – 54. V. Lakshmibai, C. Musili, and C. S. Seshadri, Geometry of \?/\?. III. Standard monomial theory for a quasi-minuscule \?, Proc. Indian Acad. Sci. Sect. A Math. Sci. 88 (1979), no. 3, 93 – 177. V. Lakshmibai, C. Musili, and C. S. Seshadri, Geometry of \?/\?. IV. Standard monomial theory for classical types, Proc. Indian Acad. Sci. Sect. A Math. Sci. 88 (1979), no. 4, 279 – 362. · Zbl 0447.14011
[7] C. S. Seshadri, Geometry of \?/\?. I. Theory of standard monomials for minuscule representations, C. P. Ramanujam — a tribute, Tata Inst. Fund. Res. Studies in Math., vol. 8, Springer, Berlin-New York, 1978, pp. 207 – 239. V. Lakshmibai and C. S. Seshadri, Geometry of \?/\?. II. The work of de Concini and Procesi and the basic conjectures, Proc. Indian Acad. Sci. Sect. A 87 (1978), no. 2, 1 – 54. V. Lakshmibai, C. Musili, and C. S. Seshadri, Geometry of \?/\?. III. Standard monomial theory for a quasi-minuscule \?, Proc. Indian Acad. Sci. Sect. A Math. Sci. 88 (1979), no. 3, 93 – 177. V. Lakshmibai, C. Musili, and C. S. Seshadri, Geometry of \?/\?. IV. Standard monomial theory for classical types, Proc. Indian Acad. Sci. Sect. A Math. Sci. 88 (1979), no. 4, 279 – 362. · Zbl 0447.14011
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