Combinatorial aspects of representation theory

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Queer Supercrystal Structure for Increasing Factorizations of Fixed-Point-Free Involution Words (Representation Theory and its Combinatorial Aspects)

Queer Supercrystal Structure for Increasing Factorizations of Fixed-Point-Free Involution Words (Representation Theory and its Combinatorial Aspects)
本稿では, 一列型BCn型Koornwinder多項式P(1r)(xla, b, c, dlq, t)と一列型BCn型単項対称多項式m(1r)(x)の間の遷移行列Cを具体的に求め, 一列型BCn型Koornwinder多項式の一列型BCn-1型Koornwinder多項式による分規則を記述する. 証明のために一列型Koornwinder多項式の退化隣接関係(degeneration scheme)を導入する. 一列型Koornwinder多項式の退化隣接関係とは, 一列型Koornwinder多項式のパラメタa, b, c, dを次のように1つずつ特殊化した多項式を考えることである: (a, b, c, d)→ (a, -a, c, d)→(a, -a, c, -c)→ (√tc, -√tc, c,
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A generalization of Lakshmibai-Seshadri paths and Chevalley formula for arbitrary weights (Representation Theory and its Combinatorial Aspects)

A generalization of Lakshmibai-Seshadri paths and Chevalley formula for arbitrary weights (Representation Theory and its Combinatorial Aspects)
本研究では, 表現論において里要な組合せ論的対象であるLakshmibai-Seshadriパスを, 一般のウェイトヘ拡張し, interpolated Lakshmibai-Seshadriパスを導入した. また, interpolated Lakshmibai-Seshadriパスを用いて, 旗多様体G/Bのトーラス同変K理論におけるChevalley公式を記述した.本稿では, これらの結果について, 証明等の詳細を省いて概説する. 本稿は, RIMS共同研究「表現論とその組合せ論的側面」における講演"A generalization of Lakshmibai-Seshadri paths and Chevalley formula for arbitraryweights"のまとめである.
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Finite size approximation for representations of $U_q(\widehat{\mathfrak{sl}}(n))$(Combinatorial Aspects in Representation Theory and Geometry)

, 1991
Michio Jimbo
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Several classes of plane partitions with the same generating function (Representation Theory and its Combinatorial Aspects)

, 2020
雅雄石川
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Relative invariants of the polynomial rings over the finite and tame type quivers(Combinatorial Aspects in Representation Theory and Geometry)

, 1991
Kazuhiko Koike
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Topological data analysis and topological deep learning beyond persistent homology: a review. [PDF]