For any finitely generated unital commutative associative algebra $\mathcal {R}$ over $\mathbb {C}$ and any complex finite-dimensional simple Lie algebra $\mathfrak {g}$ with a fixed Cartan subalgebra $\mathfrak {h}$, we classify all $\mathfrak {g}\otimes \mathcal {R}$-modules on $U(\mathfrak {h})$ such that $\mathfrak {h}$ as a subalgebra of $\mathfrak {g}\otimes \mathcal {R}$, acts on $U(\mathfrak {h})$ by the multiplication. We construct these modules explicitly and study their module structures.
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Funding
National Natural Science Foundation of China(11931009)
Anhui Initiative in Quantum Information Technologies(AHY150000)
National Natural Science Foundation of China(11771410)
RIGHTS & PERMISSIONS
School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature
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