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Falling Powers and the Algebra of Descents

Algebra and Number Theory Seminar

Falling Powers and the Algebra of Descents
Series: Algebra and Number Theory Seminar
Location: ENR2 S395
Presenter: Gotz Pfeiffer, National University of Ireland, Galway

A finite Coxeter group of classical type A, B or D contains a chain of subgroups of the same type.  We show that intersections of conjugates of these subgroups are again of the same type, and make precise in which sense and to what extent this property is exclusive to the classical types of Coxeter groups.  As the main tool for the proof we use Solomon’s descent algebra.  Using Stirling numbers, we express certain basis elements of the descent algebra as polynomials and derive explicit multiplication formulas for a commutative subalgebra of the descent algebra.  This is joint work with Linus Hellebrandt.