17,597 research outputs found
Integration over Tropical Plane Curves and Ultradiscretization
In this article we study holomorphic integrals on tropical plane curves in
view of ultradiscretization. We prove that the lattice integrals over tropical
curves can be obtained as a certain limit of complex integrals over Riemannian
surfaces.Comment: 32pages, 12figure
Grothendieck polynomials and the Boson-Fermion correspondence
In this paper we study algebraic and combinatorial properties of Grothendieck
polynomials and their dual polynomials by means of the Boson-Fermion
correspondence. We show that these symmetric functions can be expressed as a
vacuum expectation value of some operator that is written in terms of
free-fermions. By using the free-fermionic expressions, we obtain alternative
proofs of determinantal formulas and Pieri type formulas.Comment: 19 page
Solution of the generalized periodic discrete Toda equation II; Theta function solution
We construct the theta function solution to the initial value problem for the
generalized periodic discrete Toda equation.Comment: 11 page
Tropical Krichever construction for the non-periodic box and ball system
A solution for an initial value problem of the box and ball system is
constructed from a solution of the periodic box and ball system. The
construction is done through a specific limiting process based on the theory of
tropical geometry. This method gives a tropical analogue of the Krichever
construction, which is an algebro-geometric method to construct exact solutions
to integrable systems, for the non-periodic system.Comment: 13 pages, 1 figur
Two dimensional periodic box-ball system and its fundamental cycle
We study a 2-dimensional Box-Ball system which is a ultradiscrete analog of
the discrete KP equation. We construct an algorithm to calculate the
fundamental cycle, which is an important conserved quantity of the 2-dim.
Box-Ball system with periodic boundary condition, by using the tropical curve
theory.Comment: 16 pages, 5 figure
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