Characters of groups and algebras as special functions and their applications

2014 Fiscal Year Final Research Report

• Project/Area Number: 24740033
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: 防衛大学校(総合教育学群、人文社会科学群、応用科学群、電気情報学群及びシステム工学群)
• Principal Investigator: MIZUKAWA Hiroshi 防衛大学校(総合教育学群、人文社会科学群、応用科学群、電気情報学群及びシステム工, その他部局等, 准教授 (60531762)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 指標の理論 / 帯球関数

Outline of Final Research Achievements

In this study, some results are obtained by using the orthogonality of group or algebra characters. First result is related to stochastic models called Poker-dice game and Ehrenfest's urn model. Their ergodic properties and cut-off phenomenons are analyzed by using representation theoretical method. Second result is a formula on certain algebraic relations of Schur functions. Some formulas are proved by the representation of an affine Lie algebra and the theory of the symmetric functions. Furthermore the representation theoretic meaning of these formulas is revealed. The last result is a combinatorial formula of (class) regular partitions. The relation between the product of all parts of the class regular partitions and that of multiplicities are given.

Free Research Field

表現論