| Budget Amount *help |
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Outline of Final Research Achievements |
I explored applications of the representation theory of non-commutative semisimple matrix algebras, such as the Terwilliger algebra which is defined for each vertex of a graph, and obtained results, for example, about the structure and non-existence of so-called relative designs. In the process of studying applications to quantum probability theory and so on, I found new families of univariate hypergeometric Laurent orthogonal polynomials and bivariate hypergeometric orthogonal polynomials, and described their fundamental properties, such as recurrence relations. Besides, I proved a certain conjecture related to quantum information theory, with the help of a technique from algebraic combinatorics. During the period of the research plan, I also started several other projects related to quantum probability theory and information theory, etc., and I plan to publicize the outcomes whenever they are ready.
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