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Monodromy Groups and Bilinear Monodromy Invariant Combinations of Generalized Hypergeometric Type Integrals
Author(s) -
Constantinescu Florin,
Neumann Frank
Publication year - 1996
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19960310)19:4<257::aid-mma768>3.0.co;2-9
Subject(s) - mathematics , monodromy , braid group , pure mathematics , invariant (physics) , holomorphic function , hypergeometric function , type (biology) , group (periodic table) , generalized hypergeometric function , basic hypergeometric series , uniqueness , hypergeometric distribution , algebra over a field , mathematical analysis , mathematical physics , ecology , chemistry , organic chemistry , biology
The problem of determining bilinear combinations of holomorphic and antiholomorphic generalized hypergeometric type integrals left invariant under the action of the monodromy groups of the integrals is studied. In the special cases of simple Pochhammer type integrals and of twofold hypergeometric type integrals the existence and uniqueness of the bilinear invariants are proved, and the bilinear invariants are explicitly computed. Preparing the tools it is shown how to linearize and iterate representations of the braid group B n as automorphism groups of certain free subgroups of the braid group B n +1 , and how the resulting iterated linear representations of the braid group in a natural way provide an algorithm to compute the monodromy group of generalized hypergeometric type integrals. Explicit formulae for different types of integration contours are given in the case of simple and twofold integrals.