We identify the Grothendieck group of certain direct sum of singular blocks
of the highest weight category for sl(n) with the n-th tensor power of the
fundamental (two-dimensional) sl(2)-module. The action of U(sl(2)) is given by
projective functors and the commuting action of the Temperley-Lieb algebra by
Zuckerman functors. Indecomposable projective functors correspond to Lusztig
canonical basis in U(sl(2)). In the dual realization the n-th tensor power of
the fundamental representation is identified with a direct sum of parabolic
blocks of the highest weight category. Translation across the wall functors act
as generators of the Temperley-Lieb algebra while Zuckerman functors act as
generators of U(sl(2)).Comment: 31 pages, 11 figure
