arXiv subjects

Takashi Otofuji

Publications and source records attributed to Takashi Otofuji.

3 recordsLinked to original sources

arXiv2022

Positive energy representations of affine algebras and Stokes matrices of the affine Toda equations

We give a construction which produces a positive energy representation of the affine Lie algebra of type A_n from the Stokes data of a solution of the tt*-Toda equations of type A_n. The construction appears to play a role in conformal field theory. We illustrate this with several examples: the fusion ring, W-algebra minimal models (Argyres-Douglas theory), as well as topological-antitopological fusion itself. (Minor typographical changes for this version.)

math.DG↗

arXiv2006

Geodesics of Hofer's metric on the space of Lagrangian submanifolds

We study geodesics of Hofer's metric on the space of Lagrangian submanifolds in arbitrary symplectic manifolds from the variational point of view. We give a characterization of length-critical paths with respect to this metric. As a result, we prove that if two Lagrangian submanifolds are disjoint then we cannot join them by length-minimizing geodesics.

math.SG↗

arXiv2000

Quantum cohomology and the periodic Toda lattice

We describe a relation between the periodic one-dimensional Toda lattice and the quantum cohomology of the periodic flag manifold (an infinite-dimensional Kaehler manifold). This generalizes a result of Givental and Kim relating the open Toda lattice and the quantum cohomology of the finite-dimensional flag manifold. We derive a simple and explicit "differential operator formula" for the necessary quantum products, which applies both to the finite-dimensional and to the infinite-dimensional situations.

math.QA↗