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

P. V. Bushlanov; B. L. Feigin; A. M. Gainutdinov; I. Yu Tipunin

doi:10.1016/j.nuclphysb.2009.03.016

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

P. V. Bushlanov, B. L. Feigin, A. M. Gainutdinov, I. Yu Tipunin^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

29 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	179-195
Number of pages	17
Journal	Nuclear Physics B
Volume	818
Issue number	3
DOIs	https://doi.org/10.1016/j.nuclphysb.2009.03.016
State	Published - 11 Sep 2009
Externally published	Yes

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AU - Tipunin, I. Yu

PY - 2009/9/11

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

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