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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Computation of Kazhdan-Lusztig polynomials and some applications to finite groups
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by Frank Lübeck PDF
Trans. Amer. Math. Soc. 373 (2020), 2331-2347 Request permission


We discuss a practical algorithm to compute parabolic Kazhdan-Lusztig polynomials. As an application we compute Kazhdan-Lusztig polynomials which are needed to evaluate a character formula for reductive groups due to Lusztig.

Some coefficients of these polynomials have interesting interpretations for certain finite groups. We find examples of finite dimensional modules for finite groups with much higher dimensional first cohomology group than in all previously known cases.

Some of these examples lead to the construction of finite groups with many maximal subgroups, contradicting an old conjecture by G. E. Wall.

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Additional Information
  • Frank Lübeck
  • Affiliation: Lehrstuhl D für Mathematik, RWTH Aachen, Pontdriesch 14/16, D-52064 Aachen, Germany
  • MR Author ID: 362381
  • Email:
  • Received by editor(s): October 22, 2016
  • Received by editor(s) in revised form: August 4, 2017, and March 25, 2019
  • Published electronically: January 28, 2020
  • Additional Notes: The author acknowledges support from the DFG within the TRR 195
  • © Copyright 2020 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 2331-2347
  • MSC (2010): Primary 20F55, 20C08, 20G05, 20G10, 20E28
  • DOI:
  • MathSciNet review: 4069221