Geodesic
Hypergeometric functions associated with the Grassmannian $G_{3,6}$
Sbornik. Mathematics, Tome 66 (1990) no. 1, pp. 1-40 
I. M. Gel'fand; M. I. Graev. Hypergeometric functions associated with the Grassmannian $G_{3,6}$. Sbornik. Mathematics, Tome 66 (1990) no. 1, pp. 1-40. http://geodesic.mathdoc.fr/item/SM_1990_66_1_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Hypergeometric functions are studied on the variety $G_{3,6}$ of three-dimensional subspaces in $\mathbf C^6$ and on nondegenerate strata in $G_{3,6}$. They are described in the form of power series, systems of differential equations and integrals of Euler type. A connection is established between these functions and some classical hypergeometric functions of one and two variables. Figures: 1. Bibliography: 12 titles.

[1] Gelfand I. M., “Obschaya teoriya gipergeometricheskikh funktsii”, DAN SSSR, 288:1 (1986), 14–18 | MR | Zbl

[2] Gelfand I. M., Gelfand S. I., “Obobschennye gipergeometricheskie uravneniya”, DAN SSSR, 288:2 (1986), 279–283 | MR | Zbl

[3] Gelfand I. M., Graev M. I., “Teorema dvoistvennosti dlya obschikh gipergeometricheskikh funktsii”, DAN SSSR, 289:1 (1986), 19–23 | MR

[4] Gelfand I. M., Zelevinskii A. V., “Algebraicheskie i kombinatornye aspekty obschei teorii gipergeometricheskikh funktsii”, Funktsion. analiz i ego pril., 20:3 (1986), 17–34 | MR | Zbl

[5] Vasilev V. A., Gelfand I. M., Zelevinskii A. V., “Povedenie obschikh gipergeometricheskikh funktsii v kompleksnoi oblasti”, DAN SSSR, 290:2 (1986), 277–281 | MR

[6] Vasilev V. A., Gelfand I. M., Zelevinskii A. V., “Obschie gipergeometricheskie funktsii na kompleksnykh grassmanianakh”, Funktsion. analiz i ego pril., 21:1 (1987), 23–38 | MR | Zbl

[7] Gelfand I. M., Graev M. I., “Gipergeometricheskie funktsii, svyazannye s grassmanianom $G_{3,6}$”, DAH SSSR, 293:2 (1987), 288–293 | MR | Zbl

[8] Gelfand I. M., Serganova V. V., “Kombinatornye geometrii i straty tora na odnorodnykh kompaktnykh mnogoobraziyakh”, UMN, 42:2 (1987), 107–134 | MR | Zbl

[9] Gelfand I. M., Graev M. I., Zelevinskii I. V., “Golonomnye sistemy uravnenii i ryady gipergeometricheskogo tipa”, DAN SSSR, 295:1 (1987), 14–19 | Zbl

[10] Beitmen R., Erdeii A., Vysshie transtsendentnye funktsii, t. 1, Nauka, M., 1973

[11] Fam F., “Obobschennye formuly Pikara–Lefshetsa i vetvlenie integralov”, Matematika, 13:4 (1969), 61–93

[12] Pochhammer L., “Uber die Differentialgleichtmg der allgemeinen hypergeometrischen Reihe mit zwei endlichen singularen Punkten”, J. Reine Angew. Math., 102 (1988), 76–159