Abstract Young pairs for Coxeter groups of type D (extended abstract)

The notion of an Abstract Young (briefly: AY) representation is a natural generalization of the classical Young orthogonal form. The AY representations of the symmetric group are characterized in [U2]. In this paper we present several types of minimal AY representations of Dn, associated with standard D-Young tableaux which are a natural generalization of usual standard Young tableaux. We give an explicit combinatorial view (the representation space is spanned by certain standard tableaux while the action is a generalized Young orthogonal form) of representations which are induced into D _n from minimal AY representations of one of the natural embeddings of S _n into D _n. Then we show that these induced representations are isomorphic to the direct sum of two or three minimal AY representations of D _n also associated with standard D-Young tableaux. It is done by constructing a continuous path between representation matrices where one end of the path is the mentioned direct sum; while the other end is the classical form of induced an representation.