1999 Fiscal Year Final Research Report Summary
Algebro-analytic and/or representation-theoretic study of hypergeometric differential systems
| Project/Area Number |
10640146
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | HOKKAIDO UNIVERSITY |
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Principal Investigator |
SAITO Mutsumi Hokkaido Univ., Grad. School of Sci., Ass. Prof., 大学院・理学研究科, 助教授 (70215565)
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| Co-Investigator(Kenkyū-buntansha) |
SHIBUKAWA Youichi Hokkaido Univ., Grad. School of Sci., Inst., 大学院・理学研究科, 助手 (90241299)
YAMASHITA Hiroshi Hokkaido Univ., Grad. School of Sci., Ass. Prof., 大学院・理学研究科, 助教授 (30192793)
YAMADA Hiro-Fumi Hokkaido Univ., Grad. School of Sci., Ass. Prof., 大学院・理学研究科, 助教授 (40192794)
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| Project Period (FY) |
1998 – 1999
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| Keywords | hypergeometric system / holonomic system / Lie algebra / Grobner basis / Weyl algebra |
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| Research Abstract |
With support of many examples by a computer, and by communication with world-wide experts in several fields, we obtained the following results.
Mutsumi Saito has studied A-hypergeometric systems. He, in collaboration with Bernd Sturmfels and Nobuki Takayama, found and studied an unexpected relationship between A-hypergeometric systems and integer programmings, and showed the invariance of the rank of a regular holonomic system under Grobner deformations, and obtained three sufficient conditions for the rank of an A-hypergeometric system to equal the volume of the convex hull spanned by A. He classified parameters according to D-isomorphism classes of their corresponding A-hypergeometric systems.
Hiro-Fumi Yamada has studied the relationship between Q-functions and affine Lie algebras. He showed a Q-function expressed as a polynomial of power sum symmetric functions is a weight vector for the basic representation of a certain affine Lie algebra realized on the polynomial ring, and illustrated the corresponding weight by Young diagrams. He also found an unexpected relation of Schur's S-functions and Q-functions.
Hiroshi Yamashita has studied Harish-Chandra modules. He specified the embedding of Borel-de Siebenthal discrete series into the principal series representations. He also described the associated cycles of some important representations, such as discrete series and unitary highest weight representations, by using the principal symbols of invariant differential operators of gradient type whose kernels realize their dual Harish-Chandra modules.
Youichi Shibukawa has worked on Ruijsenaars-Schneider dynamical integrable system. Related to its Lax presentation, he, in collaboration with Nariya Kawazumi, obtained all meromorphic solutions to the Bruschi-Calogero differential equation.
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