Project/Area Number  10640146 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
Basic analysis

Research Institution  HOKKAIDO UNIVERSITY 
Principal Investigator 
SAITO Mutsumi Hokkaido Univ., Grad. School of Sci., Ass. Prof., 大学院・理学研究科, 助教授 (70215565)

CoInvestigator(Kenkyūbuntansha) 
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 HiroFumi Hokkaido Univ., Grad. School of Sci., Ass. Prof., 大学院・理学研究科, 助教授 (40192794)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥3,000,000 (Direct Cost : ¥3,000,000)
Fiscal Year 1999 : ¥1,400,000 (Direct Cost : ¥1,400,000)
Fiscal Year 1998 : ¥1,600,000 (Direct Cost : ¥1,600,000)

Keywords  hypergeometric system / holonomic system / Lie algebra / Grobner basis / Weyl algebra / 超幾何系 / ホロノミック系 / リー環 / グレブナー基底 / ワイル代数 
Research Abstract 
With support of many examples by a computer, and by communication with worldwide experts in several fields, we obtained the following results. Mutsumi Saito has studied Ahypergeometric systems. He, in collaboration with Bernd Sturmfels and Nobuki Takayama, found and studied an unexpected relationship between Ahypergeometric 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 Ahypergeometric system to equal the volume of the convex hull spanned by A. He classified parameters according to Disomorphism classes of their corresponding Ahypergeometric systems. HiroFumi Yamada has studied the relationship between Qfunctions and affine Lie algebras. He showed a Qfunction 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 Sfunctions and Qfunctions. Hiroshi Yamashita has studied HarishChandra modules. He specified the embedding of Borelde 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 HarishChandra modules. Youichi Shibukawa has worked on RuijsenaarsSchneider dynamical integrable system. Related to its Lax presentation, he, in collaboration with Nariya Kawazumi, obtained all meromorphic solutions to the BruschiCalogero differential equation.
