Primitive idempotents in group algebras of the Weyl groups of types \(B_n\) and \(D_n\) (Q2719418)

It is known [see, for example, \textit{B.~L.~van der Waerden}, ``Algebra'', Berlin, Springer (1937; Zbl 0016.33902)] that the irreducible representations of finite groups can be described by systems of pairwise orthogonal primitive idempotents in the corresponding group algebras. In particular, for the Weyl groups of type \(A_n\) such idempotents are called Young symmetrizers. In this paper the author obtains an explicit form of similar elements for the Weyl groups of types \(B_n\), \(C_n\) and \(D_n\). These idempotents are represented as the product of Young symmetrizers and some additional binomials. Since the Young symmetrizers can also be represented as binomial products [see \textit{D.~P.~Zhelobenko}, ``Representations of reductive Lie algebras'', Nauka, Moscow (1993; Zbl 0842.17007)], the results of this paper can be viewed as a generalization for all classical root systems.