28 citations · 209 across the 21 of their papers we have counts for
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math-ph2012★ 7 cited
Rank-3 root systems induce root systems of rank 4 via a new Clifford spinor construction
Pierre-Philippe Dechant
In this paper, we show that via a novel construction every rank-3 root system induces a root system of rank 4. Via the Cartan-Dieudonné theorem, an even number of successive Coxete…
math-ph2012★ 11 cited
A Clifford algebraic framework for Coxeter group theoretic computations
Pierre-Philippe Dechant
Real physical systems with reflective and rotational symmetries such as viruses, fullerenes and quasicrystals have recently been modeled successfully in terms of three-dimensional…
math-ph2012★ 19 cited
Clifford algebra unveils a surprising geometric significance of quaternionic root systems of Coxeter groups
Pierre-Philippe Dechant
Quaternionic representations of Coxeter (reflection) groups of ranks 3 and 4, as well as those of E_8, have been used extensively in the literature. The present paper analyses such…