Lusztig limit of quantum sl(2) at root of unity and fusion of (1,p) Virasoro logarithmic minimal models

Details Lusztig limit of quantum sl(2) at root of unity and fusion of (1,p) Virasoro logarithmic minimal models Lusztig limit of quantum sl(2) at root of unity and fusion of (1,p) Virasoro logarithmic minimal models

2009-01-12

arxiv.org/abs/0901.1602v1

Nucl.Phys.B818:179-195,2009

Physics

High Energy Physics

High Energy Physics - Theory

19 pages

Scientific paper

10.1016/j.nuclphysb.2009.03.016

We introduce a Kazhdan--Lusztig-dual quantum group for (1,p) Virasoro logarithmic minimal models as the Lusztig limit of the quantum sl(2) at pth root of unity and show that this limit is a Hopf algebra. We calculate tensor products of irreducible and projective representations of the quantum group and show that these tensor products coincide with the fusion of irreducible and logarithmic modules in the (1,p) Virasoro logarithmic minimal models.

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