Abstract:
The automorphism group of the first Weyl algebra over $\mathbb{Q}$ acts on the commuting differential operators with polynomial coefficients over $\mathbb{Q}$. We show that the orbit set is infinite for a fixed elliptic spectral curve over $\mathbb{Q}$ with at least one rational point.
Keywords:automorphism, first Weyl algebra, commuting differential operator, polynomial coefficients over $\mathbb{Q}$, elliptic spectral curve.
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