arXiv subjects

Bill Casselman

Publications and source records attributed to Bill Casselman.

2 recordsLinked to original sources

arXiv2021

A simple way to compute structure constants of semi-simple Lie algebras

The standard way to compute the structure constants of semi-simple Lie algebras involves the additive structure of the roots. In earlier work, I described how ideas of Jacques Tits could be applied to do this by using the structure of the Weyl group. In this work, I explain how to combine some of the earlier ideas with some suggestions of Kottwitz to present a very simple algorithm which comes close to constructing a canonical basis of the Lie algebra. Unfortunately, unlike previous methods, it does not work for arbitrary Kac-Moody algebra.

math.RT↗

arXiv2002

Computation in Coxeter groups II. Minimal roots

In the recent paper (Casselman, 2001) I described how a number of ideas due to Fokko du Cloux and myself could be incorporated into a reasonably efficient program to carry out multiplication in arbitrary Coxeter groups. At the end of that paper I discussed how this algorithm could be used to build the reflection table of minimal roots, which could in turn form the basis of a much more efficient multiplication algorithm. In this paper, following a suggestion of Bob Howlett, I explain how results due to Brigitte Brink can be used to construct the minimal root reflection table directly and more efficiently.

math.CO↗