Speaker: Linus Hellebrandt (Aachen)
Title: Cartan Invariants of the Descent Algebra for Coxeter Groups of Type \(A_n\)
Abstract:
We investigate the Cartan invariants of the descent algebra for Coxeter groups of type \(A_n\), using a quiver presentation of the descent algebra. We achieve an upper bound for the Cartan invariants and show that the Cartan matrix of the descent algebra for type \(A_n\) is a submatrix of the Cartan matrix of the descent algebra for type \(A_{n+1}\).