A matrix interpretation for the descent algebra of type D
Stephanie van Willigenburg
refreshments at 3:45pm
For each Coxeter group we can partition the group elements in a
certain way, and form a formal sum from the elements in each part. These formal
sums form the basis of what is known as a descent algebra. Much study has gone
into those algebras where the Coxeter group involved is either a symmetric
group or a hyperoctahedral group. A vital tool in this study has been the
existence of a "matrix interpretation" of multiplication in these algebras.
In this talk I shall formulate such a matrix interpretation for the descent
algebra of type D, and discuss results that it has suggested.
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