Coincidence of dimension and noncommutative symmetric functions

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400001
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Muroran Institute of Technology
• Principal Investigator: MORITA Hideaki 室蘭工業大学, 工学研究科, 准教授 (90435412)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 対称群 / 対称函数 / 組合せ論的ゼータ函数

Outline of Final Research Achievements

Noncommutative Macdonald polynomials are considered. The noncommutative complete symmetric functions are fundamental for the problem, and the generating function of (commutative) complete symmetric functions is a combinatorial zeta function. Thus, noncommutative combinatorial eta functions are central objects in this investigation. Constructing the noncommutative combinatorial zeta functions requires a consideration on relations of the generating functional expression, the Euler product expression, and the determinant expression. This problem is settled in a general contect, thai is, in the category of quasi-finite dynamical systems on finite digraphs. We understand that the determinant expression is the strongest among those (the generating functional expression is the weakest), and conditions are obtained for rewriting these three expressions.

Free Research Field

代数的組合せ論