N.Tsilevich and A.Vershik.
On the Fourier transform on the infinite symmetric group
Zapiski Nauchn. Semin. POMI, 325 (2005), 61-82.
English translation: J. Math. Sci. (N.Y.), 138, No. 3 (2006), 5663-5673.

Abstract. We present a sketch of the Fourier theory on the infinite symmetric group $S_\infty$. As a dual space to $S_\infty$, we suggest the space (groupoid) of Young bitableaux B. The Fourier transform of a function on the infinite symmetric group is a martingale with respect to the so-called full Plancherel measure on the groupoid of bitableaux. The Plancherel formula determines an isometry of the space $l^2(S_\infty,m)$ of square summable functions on the infinite symmetric group with the counting measure and the space $L^2(B,\tilde \mu)$ of square integrable functions on the groupoid of bitableaux with the full Plancherel measure.

Back to the list of papers