Geodesic
Irreducible modules over the Virasoro algebra
Documenta mathematica, Tome 16 (2011), pp. 709-721
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In this paper, we construct two different classes of Virasoro modules from twisting Harish-Chandra modules over the twisted Heisenberg-Virasoro algebra by an automorphism of the twisted Heisenberg-Virasoro algebra. Weight modules in the first class are some irreducible highest weight modules over the twisted Heisenberg-Virasoro algebra. The non-weight modules in the first class are irreducible Whittaker modules over the Virasoro algebra. We obtain concrete bases for all irreducible Whittaker modules (instead of a quotient of modules). This generalizes known results on Whittaker modules. The second class of modules are non-weight modules which are not Whittaker modules. We determine the irreducibility and isomorphism classes of these modules.
DOI : 10.4171/dm/349
Classification : 17B10, 17B20, 17B65, 17B66, 17B68
Mots-clés : Virasoro algebra, Whittaker module, irreducible module 
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     author = {R. L\"u and X. Guo and K. Zhao},
     title = {Irreducible modules over the {Virasoro} algebra},
     journal = {Documenta mathematica},
     pages = {709--721},
     year = {2011},
     volume = {16},
     doi = {10.4171/dm/349},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/349/}
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R. Lü; X. Guo; K. Zhao. Irreducible modules over the Virasoro algebra. Documenta mathematica, Tome 16 (2011), pp. 709-721. doi: 10.4171/dm/349

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