Remote Access Representation Theory
Green Open Access

Representation Theory

ISSN 1088-4165

 

 

Balanced semisimple filtrations for tilting modules


Author: Amit Hazi
Journal: Represent. Theory 21 (2017), 4-19
MSC (2010): Primary 20G42
DOI: https://doi.org/10.1090/ert/495
Published electronically: March 8, 2017
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ U_l$ be a quantum group at an $ l$th root of unity, obtained via Lusztig's divided powers construction. Many indecomposable 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 indecomposable tilting modules. We then show that these balanced semisimple filtrations really do exist for these tilting modules.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2010): 20G42

Retrieve articles in all journals with MSC (2010): 20G42


Additional Information

Amit Hazi
Affiliation: Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, United Kingdom
Email: A.Hazi@dpmms.cam.ac.uk

DOI: https://doi.org/10.1090/ert/495
Received by editor(s): October 11, 2016
Received by editor(s) in revised form: February 15, 2017
Published electronically: March 8, 2017
Article copyright: © Copyright 2017 American Mathematical Society