Normality of affine toric varieties associated with Hermitian symmetric spaces

Mutsumi SAITO

doi:10.2969/jmsj/04640699

Mutsumi SAITO

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JOURNAL FREE ACCESS

1994 Volume 46 Issue 4 Pages 699-724

DOI https://doi.org/10.2969/jmsj/04640699

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Published: 1994 Received: September 30, 1992 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : A1) K. Aomoto, On the vanishing of cohomology attached to certain many valued meromorphic functions, J. Math. Soc. Japan, 27 (1975), 248-255.
A2) K. Aomoto, Les équations aux différences linéaires et les integrales des fonctions multiformes, J. Fac. Sci. Univ. Tokyo, 22 (1975), 271-297; Une correction et un complément à l'article “Les équations aux différences linéaires et les integrales des fonctions multiformes”. J. Fac. Sci. Univ. Tokyo, 26 (1979), 519-523.
A3) K. Aomoto, On the structure of integrals of power product of linear functions, Sci. Papers College Gen. Ed. Univ. Tokyo, 27 (1977), 49-61.
A4) K. Aomoto, Gauss-Manin connection of integral of difference products, J. Math. Soc. Japan, 39 (1987), 191-208.
B) N. Bourbaki, Groupes et algèbres de Lie, IV, V, VI, Hermann, Paris.
G) I. M. Gelfand, General theory of hypergeometric functions, Dokl. Akad. Nauk SSSR, 288 (1986), 14-18; English translation, Soviet Math. Dokl., 33 (1987), 9-13.
GGZ) I. M. Gelfand, M.1. Graev and A. V. Zelevinsky, Holonomic system of equations and series of hypergeometric type, Dokl. Akad. Nauk SSSR, 295 (1987), 14-19; English translation, Soviet Math. Dokl., 36 (1988), 5-10.
GZK1) I. M. Gelfand, A. V. Zelevinsky and M. M. Kapranov, Equations of hypergeometric type and Newton polyhedra, Dokl. Akad. Nauk SSSR, 300 (1988), 529-534; English translation, Soviet Math. Dokl., 37 (1988), 678-683.
GZK2) I. M. Gelfand, A. V. Zelevinsky and M. M. Kapranov, Hypergeometric functions and toric varieties, Funktsional. Anal. i Prilozhen, 23 (1989), 12-26; English translation, Functional Anal. Appl., 23 (1989), 94-106.
GKZ) I. M. Gelfand, M. M. Kapranov and A. V. Zelevinsky, Generalized Euler integrals and A-hypergeometric functions, Adv. in Math., 84 (1990), 255-271.
Gr) B. Grünbaum, Convex Polytopes, Interscience, London, New York, Sydney.
H) J. Hrabowski, Multiple hypergeometric functions and simple Lie algebras SL and Sp, SIAM J. Math. Anal., 16 (1985), 876-886.
KMM) E. G. Kalnins, H. L. Manocha and W. Miller Jr., The Lie theory of two-variable hypergeometric functions, Stud. Appl. Math., 62 (1980), 143-173.
LSS) T. Levasseur, S. P. Smith and J. T. Stafford, The minimal nilpotent orbit, the Joseph ideal and differential operators, J. Algebra, 116 (1988), 480-501.
S) M. Saito, Parameter shift in normal generalized hypergeometric systems, Tohoku Math. J., 44 (1992), 523-534.
TE) G. Kempf, F. Knudsen, D. Mumford and B. Saint-Donat, Toroidal Embeddings I, Lecture Notes in Math., 339, Springer-Verlag, Berlin, Heidelberg, New York.

Right : [A1] K. Aomoto, On the vanishing of cohomology attached to certain many valued meromorphic functions, J. Math. Soc. Japan, 27 (1975), 248-255.
[A2] K. Aomoto, Les équations aux différences linéaires et les integrales des fonctions multiformes, J. Fac. Sci. Univ. Tokyo, 22 (1975), 271-297; Une correction et un complément à l'article “Les équations aux différences linéaires et les integrales des fonctions multiformes”. J. Fac. Sci. Univ. Tokyo, 26 (1979), 519-523.
[A3] K. Aomoto, On the structure of integrals of power product of linear functions, Sci. Papers College Gen. Ed. Univ. Tokyo, 27 (1977), 49-61.
[A4] K. Aomoto, Gauss-Manin connection of integral of difference products, J. Math. Soc. Japan, 39 (1987), 191-208.
[B] N. Bourbaki, Groupes et algèbres de Lie, IV, V, VI, Hermann, Paris.
[G] I. M. Gelfand, General theory of hypergeometric functions, Dokl. Akad. Nauk SSSR, 288 (1986), 14-18; English translation, Soviet Math. Dokl., 33 (1987), 9-13.
[GGZ] I. M. Gelfand, M. I. Graev and A. V. Zelevinsky, Holonomic system of equations and series of hypergeometric type, Dokl. Akad. Nauk SSSR, 295 (1987), 14-19; English translation, Soviet Math. Dokl., 36 (1988), 5-10.
[GZK1] I. M. Gelfand, A. V. Zelevinsky and M. M. Kapranov, Equations of hypergeometric type and Newton polyhedra, Dokl. Akad. Nauk SSSR, 300 (1988), 529-534; English translation, Soviet Math. Dokl., 37 (1988), 678-683.
[GZK2] I. M. Gelfand, A. V. Zelevinsky and M. M. Kapranov, Hypergeometric functions and toric varieties, Funktsional. Anal. i Prilozhen, 23 (1989), 12-26; English translation, Functional Anal. Appl., 23 (1989), 94-106.
[GKZ] I. M. Gelfand, M. M. Kapranov and A. V. Zelevinsky, Generalized Euler integrals and A-hypergeometric functions, Adv. in Math., 84 (1990), 255-271.
[Gr] B. Grünbaum, Convex Polytopes, Interscience, London, New York, Sydney.
[H] J. Hrabowski, Multiple hypergeometric functions and simple Lie algebras SL and Sp, SIAM J. Math. Anal., 16 (1985), 876-886.
[KMM] E. G. Kalnins, H. L. Manocha and W. Miller Jr., The Lie theory of two-variable hypergeometric functions, Stud. Appl. Math., 62 (1980), 143-173.
[LSS] T. Levasseur, S. P. Smith and J. T. Stafford, The minimal nilpotent orbit, the Joseph ideal and differential operators, J. Algebra, 116 (1988), 480-501.
[S] M. Saito, Parameter shift in normal generalized hypergeometric systems, Tohoku Math. J., 44 (1992), 523-534.
[TE] G. Kempf, F. Knudsen, D. Mumford and B. Saint-Donat, Toroidal Embeddings I, Lecture Notes in Math., 339, Springer-Verlag, Berlin, Heidelberg, New York.

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