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Representation Theory

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

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Counterexamples to the 0-1 Conjecture
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by Timothy J. McLarnan and Gregory S. Warrington PDF
Represent. Theory 7 (2003), 181-195 Request permission


For permutations $x$ and $w$, let $\mu (x,w)$ be the coefficient of highest possible degree in the Kazhdan-Lusztig polynomial $P_{x,w}$. It is well-known that the $\mu (x,w)$ arise as the edge labels of certain graphs encoding the representations of $S_n$. The 0-1 Conjecture states that the $\mu (x,w) \in \{0,1\}$. We present two counterexamples to this conjecture, the first in $S_{16}$, for which $x$ and $w$ are in the same left cell, and the second in $S_{10}$. The proof of the counterexample in $S_{16}$ relies on computer calculations.
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Additional Information
  • Timothy J. McLarnan
  • Affiliation: Department of Mathematics, Earlham College, Richmond, Indiana 47374
  • Email:
  • Gregory S. Warrington
  • Affiliation: Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003
  • MR Author ID: 677560
  • Email:
  • Received by editor(s): October 1, 2002
  • Received by editor(s) in revised form: March 24, 2003
  • Published electronically: May 7, 2003
  • © Copyright 2003 American Mathematical Society
  • Journal: Represent. Theory 7 (2003), 181-195
  • MSC (2000): Primary 05E15; Secondary 20F55
  • DOI:
  • MathSciNet review: 1973372