| 研究実績の概要 |
In addition to 2 papers on combinatorial representation theory being published, an additional 4 papers appeared on the arXiv preprint server, as follows.
I authored a paper on cellular subalgebras of the partition algebra. We described various diagram algebras and their representation theory using cellular algebras of Graham and Lehrer and the decomposition into half diagrams. We gave a new construction to build new cellular algebras from a general cellular algebra and subalgebras of the rook Brauer algebra that we call the cellular wreath product.
I coauthored a paper on a generalized definition for the quantum Clifford algebra introduced by Hayashi in 1990 using another parameter k that we call the twist, which was essential for my coauthor's subsequent work on quantum skew Howe duality and made a new connection with the alternative construction of Faddeev, Reshetikhin, and Takhtajan.
The second paper on rational lifting of crystal structures to study the ring of invariants was completed, building on our first paper from last year.
Lastly, the first of a series of at least 3 papers on the connection between Schubert calculus and stochastic particle processes was finished and uploaded.
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