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Representation Theory

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Character formulas for tilting modules over Kac-Moody algebras

Author: Wolfgang Soergel
Journal: Represent. Theory 2 (1998), 432-448
MSC (1991): Primary 17B70, 17B67, 17B37
Published electronically: December 28, 1998
Original Article: Represent. Theory 1 (1997)
MathSciNet review: 1663141
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Abstract: We show how to express the characters of tilting modules in a (possibly parabolic) category $\mathcal {O}$ over a Kac-Moody algebra in terms of the characters of simple highest weight modules. This settles, in lots of cases, Conjecture 7.2 of Kazhdan-Lusztig-Polynome and eine Kombinatorik für Kipp-Moduln, Representation Theory (An electronic Journal of the AMS) (1997), by the author, describing the character of tilting modules for quantum groups at roots of unity.

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Wolfgang Soergel
Affiliation: Universität Freiburg, Mathematisches Institut, Eckerstrasse 1, D-79104 Freiburg, Germany

Received by editor(s): September 10, 1998
Published electronically: December 28, 1998
Article copyright: © Copyright 1998 by the author