IRREDUCIBLE HARISH CHANDRA MODULES OVER THE DERIVATION ALGEBRAS OF RATIONAL QUANTUM TORI

LIU, GENQIANG ; ZHAO, KAIMING

Glasgow mathematical journal, Tome 55 (2013) no. 3, pp. 677-693

Résumé

Let d be a positive integer, q=(qij)d×d be a d×d matrix, Cq be the quantum torus algebra associated with q. We have the semidirect product Lie algebra $\mathfrak{g}$=Der(Cq)⋉Z(Cq), where Z(Cq) is the centre of the rational quantum torus algebra Cq. In this paper, we construct a class of irreducible weight $\mathfrak{g}$-modules $\mathcal{V}$α (V,W) with three parameters: a vector α∈Cd, an irreducible $\mathfrak{gl}$d-module V and a graded-irreducible $\mathfrak{gl}$N-module W. Then, we show that an irreducible Harish Chandra (uniformaly bounded) $\mathfrak{g}$-module M is isomorphic to $\mathcal{V}$α(V,W) for suitable α, V, W, if the action of Z(Cq) on M is associative (respectively nonzero).

Détail

DOI : 10.1017/S0017089512000845

Mots-clés : 17B10, 17B20, 17B65, 17B66, 17B68

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