Schur Orthogonality Relations for the Finitary Infinite Symmetric Group

Authors: Donley R.W.¹; Sepanski M.²

Source: Linear and Multilinear Algebra, Volume 50, Number 4, 1 January 2002 , pp. 373-377(5)

Publisher: Taylor and Francis Ltd

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Abstract:

Let S_f be the finitary infinite symmetric group. For a certain class of irreducible unitary representations of S_f, a version of Schur orthogonality relations is proved. That is, we construct an invariant inner product on the matrix coefficient space of each representation and show that matrix coefficients for distinct representations are orthogonal with respect to these norms.

Keywords: Schur orthogonality relations; Symmetric groups; Unitary representations; Matrix coefficients

Document Type: Research article

Affiliations: 1: Mathematics Department, University of North Texas, Denton, TX 76203, USA 2: Baylor University, Waco, TX 76798, USA

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