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Toshiki Nakashima

  1. Ultra-discretization of the D_4^3-Geometric Crystals to the G_2^1-Perfect Crystals.

    Пнд, 03/08/2010 - 16:01 — SomNambul
    Authors: Toshiki Nakashima, Kailash C. Misra, Mana Igarashi
    Subjects: Quantum Algebra
    Abstract

    Let g be an affine Lie algebra and g^L be its Langlands dual. It is
    conjectured that g has a positive geometric crystal whose ultra-discretization
    is isomorphic to the limit of certain coherent family of perfect crystals for
    g^L. We prove that the ultra-discretization of the positive geometric crystal
    for g = D_4^3 given by Igarashi and Nakashima is isomorphic to the limit of the
    coherent family of perfect crystals for g^L= G_2^1 constructed recently by
    Misra, Mohamad and Okado.

  2. Geometric Crystals on Flag Varieties and Unipotent Subgroups of Classical Groups.

    Чт, 03/04/2010 - 16:01 — SomNambul
    Authors: Toshiki Nakashima, Mana Igarashi
    Subjects: Quantum Algebra
    Abstract

    For a classical simple algebraic group $G$ we obtain the affirmative answer
    for the conjecture in [8] that there exists an isomorphism between the
    geometric crystal on the flag variety and the one on the unipotent subgroup
    $U^-$.

  3. Epsilon Systems on Geometric Crystals of type $A_n$.

    Чт, 11/19/2009 - 16:01 — SomNambul
    Authors: Toshiki Nakashima
    Subjects: Quantum Algebra
    Abstract

    We introduce an epsilon system on a geometric crystal of type $A_n$, which is
    a certain set of rational functions with some conditions. We shall show that
    there is a product structure and that it is invariant under the action of
    tropical R maps.

  4. Affine Geometric Crystal of type $D_4^{(3)}$.

    Чт, 11/19/2009 - 16:01 — SomNambul
    Authors: Toshiki Nakashima, Mana Igarashi
    Subjects: Quantum Algebra
    Abstract

    We shall realize certain affine geometric crystal of type $D_4^{(3)}$
    associated with the fundamental representation $W(\pi_1)$ explicitly . By its
    explicit form, we see that it has a positive structure.

  5. Admissible Pictures and Littlewood-Richardson Crystals.

    Втр, 08/18/2009 - 11:53 — SomNambul
    Authors: Toshiki Nakashima, Miki Shimojo
    Subjects: Quantum Algebra
    Abstract

    We present a one-to-one correspondence between the set of admissible pictures
    and the Littlewood-Richardson crystals. As a simple consequence, we shall show
    that the set of pictures does not depend on the choice of admissible orders.

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