Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 103, 44 pages      arXiv:1905.07713      https://doi.org/10.3842/SIGMA.2020.103

Symmetries of the Simply-Laced Quantum Connections and Quantisation of Quiver Varieties

Gabriele Rembado
Hausdorff Centre for Mathematics, Endenicher Allee 62, D-53115, Bonn, Germany

Received May 02, 2020, in final form October 13, 2020; Published online October 17, 2020; Reference [3] added November 17, 2020

Abstract
We will exhibit a group of symmetries of the simply-laced quantum connections, generalising the quantum/Howe duality relating KZ and the Casimir connection. These symmetries arise as a quantisation of the classical symmetries of the simply-laced isomonodromy systems, which in turn generalise the Harnad duality. The quantisation of the classical symmetries involves constructing the quantum Hamiltonian reduction of the representation variety of any simply-laced quiver, both in filtered and in deformation quantisation.

Key words: isomonodromic deformations; quantum integrable systems; quiver varieties; deformation quantisation; quantum Hamiltonian reduction.

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