Calculations on the Kazhdan-Lusztig Representations of S_n.

This page is a repository of some computational results from 1988 on some conjectures of Lascoux and Schützenberger on the Kazhdan-Lusztig representations of the symmetric groups.

It is now of historical interest only, having been superseded by A paper with Greg Warrington, which is where you should start.

 Here  is a PDF file containing an early version of my part of that paper.

The paper includes 2 somewhat lengthy tables of pairs of permutations. The original ASCII files containing this data are in  Table 1  and  Table 2 .

The source code used in the calculations is in klCode.tar.gz. For consistency with the McLarnan and Warrington paper, the various conditions for the counterexamples have been renumbered somewhat in the source code. This code together with Warrington's is at arXiv:math.CO/0209221 (2002).

I'm sorry to say I haven't thought about these problems in a long time; but do, please,  contact me  if you have questions.