The determinant of a hypergeometric period matrix

Houston Journal of Mathematics

Volumn 24, Issue 2, 1998, Pages 197-220

  Markov, Y ^a   Tarasov, V ^b   Varchenko, A ^a  

^a The University of North Carolina at Chapel Hill   (United States)

^b OSAKA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032425383     PISSN: 03621588     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

1. Barnabei, M., Brini, A., Rota, Dgh.-K.[G.-C]: The theory of Möbius functions, Uspekhi Mat. Nauk. 41, no.3, 113-157 (1986); English transl. in Russian Math. Surveys 41 (1986).
2. Douai, A., Terao, H.: The determinant of a hypergeometric period matrix, Invent math 128, 417-436 (1997).
3. Falk, M. J., Terao, H.: βnbc-bases for cohomology of local system on hyperplanes complements, Transactions AMS, 349, 189-202 (1997)
4. Loeser, F.: Arrangements d'hyperplans et somme de Gauss, Ann. Sci. École Norm. Sup. 24, 379-400 (1991)
5. Loeser, F. and Sabbah, C.: Equations aux différences finies et déterminants d'intégrales de fonctions multiformes, Comment. Math. Helv. 66, 458-503 (1991)
6. Orlik, P., Terao, H.: Arrangements of hyperplanes. Grundlehren der Math. Wiss. 300, Berlin Heildelberg New York: Springer, 1992.
7. Schechtman, V., Terao, H., Varchenko, A.: Local systems over complements of hyperplanes and the Kac-Kazhdan conditions for singular vectors, J. Pure Appl. Algebra 100, 93-102 (1995).
8. Schechtman, V., Varchenko, A.: Arrangements of hyperplanes and Lie algebra homology, Invent. math. 106, 139-194 (1991).
9. Tarasov, V., Varchenko, A.: Geometry of q-hypergeometric functions as a bridge between Yangians and quantum affine algebras, Invent. Math 128, 501-588 (1997).
10. Varchenko, A.: The Euler Beta-function, the Vandermonde determinant, Legendre's equation, and critical values of linear functions on a configuration of hyperplanes, Math. USSR Izvestija 35 (1990), 543-572 and 36, 155-168 (1991).
11. Varchenko, A.: The Euler Beta-function, the Vandermonde determinant, Legendre's equation, and critical values of linear functions on a configuration of hyperplanes, Math. USSR Izvestija 35 (1990), 543-572 and 36, 155-168 (1991).
12. Varchenko, A.: Multidimensional hypergeometric functions and representation theory of Lie algebras and quantum groups, Advanced Series in Mathematical Physics - 21, World Scientific Publishers, Singapore, 1995.
13. Varchenko, A.: Critical values and the deteminant of the periods, Uspekhi Mat. Nauk. 44, no.4, 235-236 (1989); English transl. in Russian Math. Surveys 44 no.4, 209-210 (1989).
14. Varchenko, A.: Critical points of the product of powers of linear functions and families of bases of singular vectors, Compositio Math. 97, 385-401 (1995).
15. Varchenko, A.: Determinant formula for Selberg-type integrals, Func.Anal.Appl. 25, no 4, 304-305 (1991).
16. Ziegler, G.: Matroid shellability, β-systems, and affine arrangements, J. Alg. Combinatorics, 1, 283-300 (1992).