On the Descent Algebra of Type $D$

Details On the Descent Algebra of Type $D$ On the Descent Algebra of Type $D$

2007-06-19

arxiv.org/abs/0706.2711v1

J. of Algebra 206:699-705 (1998)

Mathematics

Combinatorics

7 pages

Scientific paper

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, $\Sigma B_{n-2}$.

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