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Advanced Studies in Pure Mathematics 24, 1996 Progress in Algebraic Combinatorics
 

Summary: Advanced Studies in Pure Mathematics 24, 1996
Progress in Algebraic Combinatorics
pp. 0{0
Cells in aĆne Weyl groups and tilting modules
Henning Haahr Andersen
Abstract.
Let G be a reductive algebraic group over a eld of positive
characteristic. In this paper we explore the relations between the
behaviour of tilting modules for G and certain Kazhdan-Lusztig cells
for the aĆne Weyl group associated with G. In the corresponding
quantum case at a complex root of unity V. Ostrik has shown that
the weight cells de ned in terms of tilting modules coincide with
right Kazhdan-Lusztig cells. Our method consists in comparing our
modules for G with quantized modules for which we can appeal to
Ostrik's results. We show that the minimal Kazhdan-Lusztig cell
breaks up into in nitely many "modular cells" which in turn are
determined by bigger cells. At the opposite end we call attention to
recent results by T. Rasmussen on tilting modules corresponding to
the cell next to the maximal one. Our techniques also allow us to
make comparisons with the mixed quantum case where the quantum

  

Source: Andersen, Henning Haahr - Department of Mathematics, Aarhus Universitet

 

Collections: Mathematics