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arXiv · 2511.06431

Hamiltonian flow between standard module Lagrangians

Yujin Tong
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Abstract

In Aganagic's Fukaya category of the Coulomb branch of quiver gauge theory, the $T_\theta$-brane algebra gives a symplectic realization of the Khovanov-Lauda-Rouquier-Webster (KLRW) algebra, where each standard module is known to admit two Lagrangian realizations: the 'U'-shaped $T$-brane and the step $I$-brane. We show that the latter arises as the infinite-time limit of the Hamiltonian evolution of the former, thus serving as a generalized thimble. This provides a geometric realization of the categorical isomorphism previously established through holomorphic disc counting.

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Yujin Tong. 2025-11-09. Hamiltonian flow between standard module Lagrangians. https://arxiv.org/abs/2511.06431

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