A general commutative descent algebra. II: The case \(C_ n\)
In a previous paper [ibid., 990-1014 (1995; see the preceding review Zbl 0832.20060)], the author has defined a commutative algebra \({\mathcal T}(W)\) for any Weyl group \(W\). Here she investigates the case where the Weyl group is of type \(C_n\). She shows that the algebra is of dimension \(2n\) and she explicitly constructs \(2n\) orthogonal idempotents. Hence \({\mathcal T}(C_n)\) is shown to be semi-simple. She also shows that the commutative semi-simple descent algebra of dimension \(n\) described by \textit{F. Bergeron} and the reviewer [J. Pure Appl. Algebra 79, 109-129 (1992; Zbl 0793.20004)] has a natural isomorphic copy in \({\mathcal T}(C_n)\). Remark that \({\mathcal T}(C_n)\) is not isomorphic to a subalgebra of the full descent algebra.
scientific article; zbMATH DE number 794352