IRREDUCIBLE HARISH CHANDRA MODULES OVER THE DERIVATION ALGEBRAS OF RATIONAL QUANTUM TORI
2013 ◽
Vol 55
(3)
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pp. 677-693
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AbstractLet 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).
2009 ◽
Vol 06
(04)
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pp. 555-572
2016 ◽
Vol 15
(09)
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pp. 1650174
Keyword(s):
2002 ◽
Vol 45
(4)
◽
pp. 672-685
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Keyword(s):
2006 ◽
Vol 08
(02)
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pp. 135-165
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2007 ◽
Vol 3
(1)
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pp. 119-131
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2010 ◽
Vol 62
(2)
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pp. 382-399
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