Geodesic
Representations of Quantum Heisenberg Algebras
Canadian journal of mathematics, Tome 46 (1994) no. 5, pp. 920-929

Voir la notice de l'article provenant de la source Cambridge University Press

A Lie algebra is called a Heisenberg algebra if its centre coincides with its derived algebra and is one-dimensional. When is infinite-dimensional, Kac, Kazhdan, Lepowsky, and Wilson have proved that -modules that satisfy certain conditions are direct sums of a canonical irreducible submodule. This is an algebraic analogue of the Stone-von Neumann theorem. In this paper, we extract quantum Heisenberg algebras, q (), from the quantum affine algebras whose vertex representations were constructed by Frenkel and Jing. We introduce the canonical irreducible q ()-module Mq and a class Cq of q ()-modules that are shown to have the Stone-von Neumann property. The only restriction we place on the complex number q is that it is not a square root of 1. If q 1 and q 2 are not roots of unity, or are both primitive m-th roots of unity, we construct an explicit isomorphism between q 1() and q 2(). If q 1 is a primitive m-th root of unity, m odd, q 2 a primitive 2m-th or a primitive 4m-th root of unity, we also construct an explicit isomorphism between q 1() and q 2().
DOI : 10.4153/CJM-1994-052-7
Mots-clés : 17B37, 17B65 
Fabbri, Marc A.; Okoh, Frank. Representations of Quantum Heisenberg Algebras. Canadian journal of mathematics, Tome 46 (1994) no. 5, pp. 920-929. doi: 10.4153/CJM-1994-052-7
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