Faculty (2000)

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)).