41 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
On flagged -theoretic symmetric polynomials
We provide a fermionic description of flagged skew Grothendieck polynomials,
which can be seen as a -theoretic counterpart of flagged skew Schur
polynomials. Our proof relies on the Jacobi-Trudi type formula established by
Matsumura. This result generalizes the author's previous works on a fermionic
description of skew Grothendieck polynomials and multi-Schur functions.Comment: 8page