Products and symmetrized powers of irreducible representations of Sp(2n, R) and their associates

King, R.C. and Wybourne, B.G. (1998) Products and symmetrized powers of irreducible representations of Sp(2n, R) and their associates. Journal of Physics A: Mathematical and General, 31 (31), 6669-6689. (doi:10.1088/0305-4470/31/31/013).

Record type: Article

Abstract

The calculation of Kronecker products and plethysms of the infinite-dimensional harmonic series unitary irreducible representations of the non-compact group (Sp (2n, r) is considered. The complementarity of (Sp (2n, r) and O(k) is used to define associate irreducible representations of (Sp (2n, r). This leads to simple relationships between Kronecker products and plethysms of irreducible representations of (Sp (2n, r) and those of their corresponding associate irreducible representations. In the process of proving the validity of these previously conjectured relationships several new identities are found for plethysms involving infinite series of Schur functions. In addition, a general formula for plethysms of arbitrary irreducible representations of (Sp (2n, r) is derived and its mplementation is illustrated with a detailed example. A remarkable analogy is then observed between plethysms of the basic harmonic irreducible representations of (Sp (2n, r) and those of the basic spin irreducible representations of SO(2n).

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