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Yasuhiko Yamada

  1. Lax formalism for q-Painleve equations with affine Weyl group symmetry of type E^{(1)}_n.

    Втр, 04/13/2010 - 15:01 — SomNambul
    Authors: Yasuhiko Yamada
    Subjects: Mathematical Physics
    Abstract

    An explicit form of the Lax pair for the q-difference Painleve equation with
    affine Weyl group symmetry of type E^{(1)}_8 is obtained. Its degeneration to
    E^{(1)}_7, E^{(1)}_6 and D^{(1)}_5 cases are also given.

  2. Generalized energies and integrable D^{(1)}_n cellular automaton.

    Ср, 01/13/2010 - 16:01 — SomNambul
    Authors: Atsuo Kuniba, Reiho Sakamoto, Yasuhiko Yamada
    Subjects: Quantum Algebra
    Abstract

    We introduce generalized energies for a class of U_q(D^{(1)}_n) crystals by
    using the piecewise linear functions that are building blocks of the
    combinatorial R. They include the conventional energy in the theory of affine
    crystals as a special case. It is shown that the generalized energies count the
    particles and anti-particles in a quadrant of the two dimensional lattice
    generated by time evolutions of an integrable D^{(1)}_n cellular automaton.
    Explicit formulas are conjectured for some of them in the form of ultradiscrete
    tau functions.

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