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arXiv · 1711.08031

Singular vector structure of quantum curves

Paweł Ciosmak·Leszek Hadasz·Masahide Manabe·Piotr Sułkowski
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Abstract

We show that quantum curves arise in infinite families and have the structure of singular vectors of a relevant symmetry algebra. We analyze in detail the case of the hermitian one-matrix model with the underlying Virasoro algebra, and the super-eigenvalue model with the underlying super-Virasoro algebra. In the Virasoro case we relate singular vector structure of quantum curves to the topological recursion, and in the super-Virasoro case we introduce the notion of super-quantum curves. We also discuss the double quantum structure of the quantum curves and analyze specific examples of Gaussian and multi-Penner models.

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Paweł Ciosmak, Leszek Hadasz, Masahide Manabe, Piotr Sułkowski. 2017-11-21. Singular vector structure of quantum curves. https://arxiv.org/abs/1711.08031

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