2000/02/11 by Joseph Bernstein, Igor Frenkel, Mikhail Khovanov
Mathematics · #math.QA #math.RT #msc:17B10
published as Selecta Mathematica, New ser. 5 (1999) 199--241 · 31 pages, 11 figures
arxiv created 2000/02/11 · arxiv updated 2009/11/30
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)).