Study of generating functions viewed from group theory and category theory

点击翻译按钮获取中文摘要

1.Asai-Yoshida's conjecture on the number of group homomorphisms has a connection with p-adic anallysis (Yoshida, Takegahara, K.Conrad, etc.). Furthermore, Yoshida solved the conjecture for the homomorphisms from the fundamental group of a compact Riemann surface whose importence in quantum field theory was pointed by M.Mulase.2.Yoshida and Oda accomplished a fundamental theory of crossed Burnside rings of finite groups.3.Yoshida, Sasaki, Oda study cohomology theory of finite groups, especially Hochschild cohomology, crossed Mackey functors and quantum doubles of group algebra.4.Yoshida, Bannai and Keisuke Shiromoto sutudies combinatorics, in particular, distance regular graphs, designs and code theory, especially an application of homological algebra to the theory of codes on a ring.5.Koshitani studies modular representation thoery of finite groups and gave an affirmative answer to the Broue conjecture for groups with some special defect groups.6.Nakamura and Yamashita studied some related areas (algebraic geometry and representation theory) and gave some interested results, especially a relation with finite simple groups.7.We invited three mathematicians from abroad.・2001 FAN Yun(Wuhan U.) Talk on Broue conjecture(Kyushu Univ.)・2003 Keith CONRAD(Connecticut U.) Talk of p-adic analysis, number theory(Hokkaido U., Kyoto U.)・2004 Segre BOUC(CNRS) Talk on Dade groups and Burnside rings (Hokaido U., Kyoto U.)A large number of results of this research has been printed and published. The remainder results will be serially published. The investigator gave some talks related to this research in some conferences--"Generating functions and related topics" (Sapporo 2001), "20-th Symposium on Algebraic Combinatorics (Kyoto 2002), "Extended Group Seminar" (Sapporo 2002,2004, and so on.