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Theoretical and Mathematical Physics

, Volume 159, Issue 1, pp 424–447 | Cite as

A differential U-module algebra for U = Ū q sℓ(2) at an even root of unity

  • A. M. SemikhatovEmail author
Article

Abstract

We show that the full matrix algebra Mat p() is a U-module algebra for U = Ū q sℓ(2), a quantum sℓ(2) group at the 2pth root of unity. The algebra Mat p() decomposes into a direct sum of projective U-modules P n + with all odd n, 1 ≤ n ≤ p. In terms of generators and relations, this U-module algebra is described as the algebra of q-differential operators “in one variable” with the relations ∂z = qq 1 + q 2 z∂ and zp = ∂p = 0. These relations define a “parafermionic” statistics that generalizes the fermionic commutation relations. By the Kazhdan-Lusztig duality, it is to be realized in a manifestly quantum-group-symmetric description of (p, 1) logarithmic conformal field models. We extend the Kazhdan-Lusztig duality between U and the (p, 1) logarithmic models by constructing a quantum de Rham complex of the new U-module algebra and discussing its field theory counterpart.

Keywords

quantum group parafermionic statistics U-module algebra Kazhdan-Lusztig duality logarithmic conformal field theory 

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Copyright information

© MAIK/Nauka 2009

Authors and Affiliations

  1. 1.Lebedev Physical InstituteRASMoscowRussia

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