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    Article

    Pfaffian identities and Virasoro operators

    A formula for Schur Q-functions is presented which describes the action of the Virasoro operators. For a strict partition \(\lambda =(\lambda _1,\lambda _2,\ldots ,\lambda _{2m})\)λ=(λ1,λ2,…,λ2m), we show that, f...

    Kazuya Aokage, Eriko Shinkawa, Hiro-Fumi Yamada in Letters in Mathematical Physics (2020)

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    Article

    Schur Function Identities Arising From the Basic Representation of \({A^{(2)}_{2}}\)

    A Lie theoretic interpretation is given for some formulas of Schur functions and Schur Q-functions. Two realizations of the basic representation of the Lie algebra

    Hiroshi Mizukawa, Tatsuhiro Nakajima, Ryoji Seno… in Letters in Mathematical Physics (2014)

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    Article

    Combinatorics for Graded Cartan Matrices of the Iwahori-Hecke Algebra of Type A

    Combinatorics concerning graded Cartan matrices for the Iwahori-Hecke algebra of type A is investigated. We give several descriptions for the determinant of the graded Cartan matrix, which imply some combinatoria...

    Masanori Ando, Takeshi Suzuki, Hiro-Fumi Yamada in Annals of Combinatorics (2013)

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    Article

    Compound Basis Arising from the Basic \({A^{(1)}_{1}}\) -Module

    A new basis for the polynomial ring of infinitely many variables is constructed which consists of products of Schur functions and Q-functions. The transition matrix from the natural Schur function basis is invest...

    Kazuya Aokage, Hiroshi Mizukawa, Hiro-Fumi Yamada in Letters in Mathematical Physics (2008)

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    Article

    Polynomial τ-Functions of the NLS-Toda Hierarchy and the Virasoro Singular Vectors

    A family of polynomial τ-functions for the NLS-Toda hierarchy is constructed. The hierarchy is associated with the homogeneous vertex operator representation of the affine algebra

    Takeshi Ikeda, Hiro-Fumi Yamada in Letters in Mathematical Physics (2002)