On the Descent Algebra of Type $D$

N. Bergeron, S. J. van Willigenburg

Published 2007-06-19Version 1

Here we give a combinatorial interpretation of Solomon's rule for multiplication in the descent algebra of Weyl groups of type $D$, $\Sigma D_n$. From here we show that $\Sigma D_n$ is a homomorphic image of the descent algebra of the hyperoctahedral group, $\Sigma B_{n-2}$.