University of the Ryukyus · Faculty of Science · 教授

Research keywordsRepresentation Theory・Nilpotent Endomorphisms・Invariant Subspaces・Orbital Varieties・Algebraic Combinatorics・Littlewood-Richardson Tableaux

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• On expected waiting time until given words appear in random sequence2023 · We provide a formula for the expected waiting time more than one words appear among given words in a random sequence, and show that distributions of random variables of waiting times and their reversals are the same.
• Correspondence between orbital varieties and sets of subspaces stable under nilpotent endomorphism2020 · From the bijective correspondence between standard tableaux T of shape \lambda and left LR words L of weight \lambda^*, we show that generic points of orbital variety V_T and set X(T_L) of subspaces stable under a nilpotent linear endomorphism describe each other. As a resuclt, ordering defined by inclusions of closures correspond.
• The bundaries of the sets of subspaces stable under a nilpotent linear transformation2018 · Let f: V\to V be the nilpotent endomorophism of Jordan type \la and T be an LR tableau of shape \la/\mu and weight \nu. We investigate boundaries of X(T) in Grasmannain G(V,n) consistsing of f-stable subspaces W of dimension n in V with Jordan type of V/W and W equal to \mu and \nu, respectively.
• LR-fillings and partial ordering of LR-tableaux2014 · Takashi Maed

• Kempf複体の超判別式への応用2002 · 基盤研究(C)
• 代数多様体上の2次線束の構成についての研究1994 · 奨励研究(A)
• 単有理関数体における有理性と非有理性を区別する不変量についての研究1992 · 奨励研究(A)

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