Critical points of the product of powers of linear functions and families of bases of singular vectors
Compositio Mathematica, Tome 97 (1995) no. 3, pp. 385-401.
@article{CM_1995__97_3_385_0,
     author = {Varchenko, A.},
     title = {Critical points of the product of powers of linear functions and families of bases of singular vectors},
     journal = {Compositio Mathematica},
     pages = {385--401},
     publisher = {Kluwer Academic Publishers},
     volume = {97},
     number = {3},
     year = {1995},
     mrnumber = {1353281},
     zbl = {0842.17044},
     language = {en},
     url = {http://www.numdam.org/item/CM_1995__97_3_385_0/}
}
TY  - JOUR
AU  - Varchenko, A.
TI  - Critical points of the product of powers of linear functions and families of bases of singular vectors
JO  - Compositio Mathematica
PY  - 1995
SP  - 385
EP  - 401
VL  - 97
IS  - 3
PB  - Kluwer Academic Publishers
UR  - http://www.numdam.org/item/CM_1995__97_3_385_0/
LA  - en
ID  - CM_1995__97_3_385_0
ER  - 
%0 Journal Article
%A Varchenko, A.
%T Critical points of the product of powers of linear functions and families of bases of singular vectors
%J Compositio Mathematica
%D 1995
%P 385-401
%V 97
%N 3
%I Kluwer Academic Publishers
%U http://www.numdam.org/item/CM_1995__97_3_385_0/
%G en
%F CM_1995__97_3_385_0
Varchenko, A. Critical points of the product of powers of linear functions and families of bases of singular vectors. Compositio Mathematica, Tome 97 (1995) no. 3, pp. 385-401. http://www.numdam.org/item/CM_1995__97_3_385_0/

[A1] Aomoto, K.: On the structure of integrals of power product of linear functions, Sc. Papers of the College of General Education. Tokyo Univ. 27 (1977) 49-61. | MR | Zbl

[A2] Aomoto, K.: On the complex Selberg integral, Q. J. Math. Oxford 38 (1987) 385-399. | MR | Zbl

[As] Askey, R.S.: Some basic hypergeometric extensions of integrals of Selberg and Andrews, SIAM J. Math. 11 (1980) 938-951. | MR | Zbl

[BBR] Barnabei, M., Brini, A. and Rota, G.-C.: Theory of Mobius functions, Uspehi Mat. Nauk. 41 (1986) no. 3, 113-157. | MR | Zbl

[BBK] Bernstein, B., Kushnirenko, A. and Khovansky, A.: Newton polytopes, Uspehi Mat. Nauk. 31 (1976) no. 3, 201-202. | MR | Zbl

[BV] Brylawski, T. and Varchenko, A.: Determinant formula for the bilinear form of a matroid (Preprint) 1993 will appear in Adv. in Math. | Zbl

[DF1] Dotsenko, V. and Fateev, V.: Conformal algebra and multipoint correlation functions in 2D statistical models, Nucl. Phys. B240 (1984) 312-348.

[DF2] Dotsenko, V. and Fateev, V.: Four-point correlation functions and the operator algebra in 2D conformal invariant theories with central charge c ≤ 1, Nucl. Phys. B251 (1985) 691-734.

[G] Gelfand, I.M.: General theory of hypergeometric functions, Dokl. Akad. Nauk. SSSR 288 (1986) 573-576. | MR | Zbl

[Ga] Gaudin, M.: Diagonalization d'une classe d'hamiltoniens de spin, Journ. de Physique 37 (1976) no. 10, 1087-1098. | MR

[K] Korepin, V.: Calculation of Norms of Bethe Wave Functions, Comm. Math. Phys. 86 (1982) 391-418. | MR | Zbl

[L] Loeser, F.: Arrangements d'hyperplans et sommes de Gauss, Ann. Scient. Ec. Norm. Sup. 24 (1991) 379-400. | Numdam | MR | Zbl

[LS] Loeser, F. and Sabbah, C.: Equations aux differences finies et determinants d'integrales de fonctions multiformes, Comment. Math. Helv. 66 (1991) 345-361. | MR | Zbl

[M] Mehta, M.: Random Matrices, Acad. Press, 1991. | MR | Zbl

[OS] Orlik, P. and Solomon, L.: Combinatorics and Topology of Complements of Hyperplanes, Invent. Math. 56 (1980) 167-189. | MR | Zbl

[RV] Reshetikhin, N. and Varchenko, A.: Quasiclassical Asymptotics of Solutions of the KZ Equations (Preprint) 1993.

[SV] Schechtman, V. and Varchenko, A.: Arrangements of hyperplanes and Lie algebra homology, Invent. Math. 106 (1991) 139-194. | MR | Zbl

[S] Selberg, A.: Bemerkninger om et multiplet integral, Norsk. Mat. Tidsskr. 26 (1994) 71-78. | MR | Zbl

[Sz] Szego, G.: Orthogonal Polynomials, AMS, 1939.

[V1] Varchenko, A.: The Euler beta-function, the Vandermonde determinant, the Legendre equation, and critical values of linear function on a configuration of hyperplanes, I, Math. USSR-Izv. 35 (1990) 543-571; II, Math. USSR-Izv. 36 (1991) 155-168. | MR | Zbl

[V2] Varchenko, A.: Determinant formula for Selberg type integrals, Funct. Analysis and its Appl. 25 (1991) no. 4, 88-89. | MR | Zbl

[V3] Varchenko, A.: Critical values and determinant of periods, Uspehi Mat. Nauk. 44 (1987) 235-236. | MR | Zbl

[V4] Varchenko, A.: Multidimensional hypergeometric functions and representation theory of Lie algebras and quantum groups Advanced Series in Math. Physics - Vol. 21, World Scientific Publ., 1995. | MR | Zbl