Critical points of the product of powers of linear functions and families of bases of singular vectors
Compositio Mathematica (1995)
- Volume: 97, Issue: 3, page 385-401
- ISSN: 0010-437X
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topVarchenko, A.. "Critical points of the product of powers of linear functions and families of bases of singular vectors." Compositio Mathematica 97.3 (1995): 385-401. <http://eudml.org/doc/90390>.
@article{Varchenko1995,
author = {Varchenko, A.},
journal = {Compositio Mathematica},
keywords = {Shapovalov form; Knizhnik-Zamolodchikov equation; quasiclassical asymptotics; singular vectors; Shapovalov norm; Bethe eigenvectors; Gaudin model},
language = {eng},
number = {3},
pages = {385-401},
publisher = {Kluwer Academic Publishers},
title = {Critical points of the product of powers of linear functions and families of bases of singular vectors},
url = {http://eudml.org/doc/90390},
volume = {97},
year = {1995},
}
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
PB - Kluwer Academic Publishers
VL - 97
IS - 3
SP - 385
EP - 401
LA - eng
KW - Shapovalov form; Knizhnik-Zamolodchikov equation; quasiclassical asymptotics; singular vectors; Shapovalov norm; Bethe eigenvectors; Gaudin model
UR - http://eudml.org/doc/90390
ER -
References
top- [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. Zbl0384.35045MR590052
- [A2] Aomoto, K.: On the complex Selberg integral, Q. J. Math. Oxford38 (1987) 385-399. Zbl0639.33002MR916224
- [As] Askey, R.S.: Some basic hypergeometric extensions of integrals of Selberg and Andrews, SIAM J. Math.11 (1980) 938-951. Zbl0458.33002MR595822
- [BBR] Barnabei, M., Brini, A. and Rota, G.-C.: Theory of Mobius functions, Uspehi Mat. Nauk.41 (1986) no. 3, 113-157. Zbl0615.05006MR854241
- [BBK] Bernstein, B., Kushnirenko, A. and Khovansky, A.: Newton polytopes, Uspehi Mat. Nauk.31 (1976) no. 3, 201-202. Zbl0354.14001MR492376
- [BV] Brylawski, T. and Varchenko, A.: Determinant formula for the bilinear form of a matroid (Preprint) 1993 will appear in Adv. in Math. Zbl0918.05038
- [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. SSSR288 (1986) 573-576. Zbl0645.33010MR841131
- [Ga] Gaudin, M.: Diagonalization d'une classe d'hamiltoniens de spin, Journ. de Physique37 (1976) no. 10, 1087-1098. MR421442
- [K] Korepin, V.: Calculation of Norms of Bethe Wave Functions, Comm. Math. Phys.86 (1982) 391-418. Zbl0531.60096MR677006
- [L] Loeser, F.: Arrangements d'hyperplans et sommes de Gauss, Ann. Scient. Ec. Norm. Sup.24 (1991) 379-400. Zbl0764.14021MR1123557
- [LS] Loeser, F. and Sabbah, C.: Equations aux differences finies et determinants d'integrales de fonctions multiformes, Comment. Math. Helv.66 (1991) 345-361. Zbl0760.39001MR1120656
- [M] Mehta, M.: Random Matrices, Acad. Press, 1991. Zbl0780.60014MR1083764
- [OS] Orlik, P. and Solomon, L.: Combinatorics and Topology of Complements of Hyperplanes, Invent. Math.56 (1980) 167-189. Zbl0432.14016MR558866
- [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. Zbl0754.17024MR1123378
- [S] Selberg, A.: Bemerkninger om et multiplet integral, Norsk. Mat. Tidsskr.26 (1994) 71-78. Zbl0063.06870MR18287
- [Sz] Szego, G.: Orthogonal Polynomials, AMS, 1939. Zbl65.0278.03
- [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. Zbl0709.33002MR1039962
- [V2] Varchenko, A.: Determinant formula for Selberg type integrals, Funct. Analysis and its Appl.25 (1991) no. 4, 88-89. Zbl0739.33012MR1167731
- [V3] Varchenko, A.: Critical values and determinant of periods, Uspehi Mat. Nauk.44 (1987) 235-236. Zbl0716.32024MR1023108
- [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. Zbl0951.33001MR1384760
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