A Family of Irreducible Representations of the Witt Lie Algebra with Infinite-Dimensional Weight Spaces
Tóm tắt
We define a 4-parameter family of generically irreducible and inequivalent representations of the Witt Lie algebra on which the infinitesimal rotation operator acts semisimply with infinite-dimensional eigenspaces. They are deformations of the (generically indecomposable) representations on spaces of polynomial differential operators between two spaces of tensor densities on S
1, which are constructed by composing each such differential operator with the action of a rotation by a fixed angle.
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