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arXiv · hep-th/0012224

Indecomposable U_q(sl_n) modules for q^h = -1 and BRS intertwiners

Paolo Furlan·Ludmil Hadjiivanov·Ivan Todorov
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Abstract

A class of indecomposable representations of U_q(sl_n) is considered for q an even root of unity (q^h = -1) exhibiting a similar structure as (height h) indecomposable lowest weight Kac-Moody modules associated with a chiral conformal field theory. In particular, U_q(sl_n) counterparts of the Bernard-Felder BRS operators are constructed for n=2,3. For n=2 a pair of dual d_2(h) = h dimensional U_q(sl_2) modules gives rise to a 2h-dimensional indecomposable representation including those studied earlier in the context of tensor product expansions of irreducible representations. For n=3 the interplay between the Poincare'-Birkhoff-Witt and (Lusztig) canonical bases is exploited in the study of d_3(h) = h(h+1)(2h+1)/6 dimensional indecomposable modules and of the corresponding intertwiners.

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Paolo Furlan, Ludmil Hadjiivanov, Ivan Todorov. 2000-12-22. Indecomposable U_q(sl_n) modules for q^h = -1 and BRS intertwiners. https://doi.org/10.1088/0305-4470%2F34%2F23%2F306

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