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Irreducibility of the monodromy representation of Lauricella's F-C
| Title: | Irreducibility of the monodromy representation of Lauricella's F-C |
| Authors: | Goto, Yoshiaki Browse this author | | Matsumoto, Keiji Browse this author →KAKEN DB |
| Keywords: | Monodromy representation | | Hypergeometric functions | | Lauricella's F-C |
| Issue Date: | Oct-2019 |
| Publisher: | Dept. of Mathematics, Faculty of Science, Hokkaido University |
| Journal Title: | Hokkaido mathematical journal (HMJ) |
| Volume: | 48 |
| Issue: | 3 |
| Start Page: | 489 |
| End Page: | 512 |
| Publisher DOI: | 10.14492/hokmj/1573722015 |
| Abstract: | Let E-C be the hypergeometric system of differential equations satisfied by Lauricella's hypergeometric series F-C of m variables. This system is irreducible in the sense of D-modules if and only if 2(m+1) non-integral conditions for parameters are satisfied. We find a linear transformation of the classically known 2(m) solutions so that the transformed ones always form a fundamental system of solutions under the irreducibility conditions. By using this fundamental system, we give an elementary proof of the irreducibility of the monodromy representation of E-C. When one of the conditions is not satisfied, we specify a non-trivial invariant subspace, which implies that the monodromy representation is reducible in this case. |
| Type: | article |
| URI: | http://hdl.handle.net/2115/76461 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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