Geodesic
IRREDUCIBLE HARISH CHANDRA MODULES OVER THE DERIVATION ALGEBRAS OF RATIONAL QUANTUM TORI
Glasgow mathematical journal, Tome 55 (2013) no. 3, pp. 677-693

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DOI

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).
DOI : 10.1017/S0017089512000845
Mots-clés : 17B10, 17B20, 17B65, 17B66, 17B68 
LIU, GENQIANG; ZHAO, KAIMING. IRREDUCIBLE HARISH CHANDRA MODULES OVER THE DERIVATION ALGEBRAS OF RATIONAL QUANTUM TORI. Glasgow mathematical journal, Tome 55 (2013) no. 3, pp. 677-693. doi: 10.1017/S0017089512000845
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     author = {LIU, GENQIANG and ZHAO, KAIMING},
     title = {IRREDUCIBLE {HARISH} {CHANDRA} {MODULES} {OVER} {THE} {DERIVATION} {ALGEBRAS} {OF} {RATIONAL} {QUANTUM} {TORI}},
     journal = {Glasgow mathematical journal},
     pages = {677--693},
     year = {2013},
     volume = {55},
     number = {3},
     doi = {10.1017/S0017089512000845},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089512000845/}
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