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- Title
Some problems of hypergeometric integrals associated with hypersphere arrangement.
- Authors
Kazuhiko AOMOTO; Yoshinori MACHIDA
- Abstract
Then dimensional hypergeometric integrals associated with a hypersphere arrangement S are formulated by the pairing of n dimensional twisted cohomology HΔn(X,Ω(*S)) and its dual. Under the condition of general position there are stated some results and conjectures which concern a representation of the standard form by a special basis of the twisted cohomology, the variational formula of the corresponding integral in terms of special invariant 1-forms using Calyley-Menger minor determinants, a connection relation of the unique twisted n-cycle identified with the unbounded chamber to a special basis of twisted n-cycles identified with bounded chambers. General conjectures are presented under a much weaker assumption.
- Subjects
HYPERGEOMETRIC functions; COHOMOLOGY theory; HYPERSPHERICAL method; INTEGRALS; DETERMINANTS (Mathematics)
- Publication
Proceedings of the Japan Academy, Series A: Mathematical Sciences, 2015, Vol 91, Issue 6, p77
- ISSN
0386-2194
- Publication type
Article
- DOI
10.3792/pjaa.91.77