The paper gives the first representation-theoretic study of the BCCA, with irreducibility criteria for restricted BMS3 massive modules and for new Whittaker modules.
Quasi-Whittaker modules
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abstract
In this paper, a general setting is proposed to define a class of modules over nonsemisimple Lie algebras $\mathfrak{g}$ induced by a nonperfect ideal $\mathfrak{p}$. This class of Lie algebras includes many well-known Lie algebras, and some of this class of modules are Whittaker modules and others are not. We call these modules quasi-Whittaker modules. By introducing a new concept: the Whittaker annihilator for universal quasi-Whittaker modules, we are able to determine the necessary and sufficient conditions for the irreducibility of the universal quasi-Whittaker modules. In the reducible case, we can obtain some maximal submodules. In particular, we classify the irreducible quasi-Whittaker modules for many Lie algebras, and obtain a lot of irreducible smooth $\mathcal{W}_n^+$-modules of height $2$.
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On the boundary Carrollian conformal algebra
The paper gives the first representation-theoretic study of the BCCA, with irreducibility criteria for restricted BMS3 massive modules and for new Whittaker modules.