On the Left Connected Subalgebra of the Descent Algebra of a Coxeter Group of Classical Type
On the Left Connected Subalgebra of the Descent Algebra of a Coxeter Group of Classical Type
Abstract A Coxeter group of classical type $$A_n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>A</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> , $$B_n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> or $$D_n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>D</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> contains a chain of subgroups of the same type. We show that intersections of conjugates of these …