Indecomposable Uq(sl(n)) modules for q(h) =-1 and BRS intertwiners

Citation
P. Furlan et al., Indecomposable Uq(sl(n)) modules for q(h) =-1 and BRS intertwiners, J PHYS A, 34(23), 2001, pp. 4857-4880
Citations number
40
Categorie Soggetti
Physics
Journal title
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
ISSN journal
03054470 → ACNP
Volume
34
Issue
23
Year of publication
2001
Pages
4857 - 4880
Database
ISI
SICI code
0305-4470(20010615)34:23<4857:IUMFQ=>2.0.ZU;2-T
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 (heig ht h) indecomposable lowest weight Kac-Moody modules associated with chiral conformal field theory. In particular, U-q(sl(n)) counterparts of the Bern ard-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-dimensio nal indecomposable representation including those studied earlier in the co ntext of tenser-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 ind ecomposable modules and of the corresponding intertwiners.