Balanced semisimple filtrations for tilting modules

2015/10/09 by Hazi, Amit
#20G42 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1510.02596

Abstract

Let U_l be a quantum group at an lth root of unity. Many tilting modules for U_l have been shown to have what we call a balanced semisimple filtration, or a Loewy series whose semisimple layers are symmetric about some middle layer. The existence of such filtrations suggests a remarkably straightforward algorithm for calculating these characters if the irreducible characters are already known. We first show that the results of this algorithm agree with Soergel's character formula for the regular tilting modules. We then show that these balanced semisimple filtrations really do exist for these tilting modules.

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