Đề tài " Hilbert series, Howe duality and branching for classical groups "

An extension of the Littlewood Restriction Rule is given that covers all pertinent parameters and simplifies to the original under Littlewood’s hypotheses. Two formulas are derived for the Gelfand-Kirillov dimension of any unitary highest weight representation occurring in a dual pair setting, one in terms of the dual pair index and the other in terms of the highest weight.