On the Fourier transform on the infinite symmetric group

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On the Fourier transform on the infinite symmetric group. / Vershik, A. M.; Tsilevich, N. V.

In: Journal of Mathematical Sciences , Vol. 138, No. 3, 01.10.2006, p. 5663-5673.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{925e1375da8247e3b587f23edbb7f4f7,

title = "On the Fourier transform on the infinite symmetric group",

abstract = "We present a sketch of the Fourier theory on the in.nite symmetric group S ∞. As a dual space to S ∞, 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 ∞, m) of square summable functions on the infinite symmetric group with the counting measure and the space L2(B,μ{\~ }) of square integrable functions on the groupoid of bitableaux with the full Plancherel measure.",

author = "Vershik, {A. M.} and Tsilevich, {N. V.}",

year = "2006",

month = oct,

day = "1",

doi = "10.1007/s10958-006-0334-0",

language = "English",

volume = "138",

pages = "5663--5673",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "3",

}

RIS

TY - JOUR

T1 - On the Fourier transform on the infinite symmetric group

AU - Vershik, A. M.

AU - Tsilevich, N. V.

PY - 2006/10/1

Y1 - 2006/10/1

N2 - We present a sketch of the Fourier theory on the in.nite symmetric group S ∞. As a dual space to S ∞, 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 ∞, m) of square summable functions on the infinite symmetric group with the counting measure and the space L2(B,μ ̃) of square integrable functions on the groupoid of bitableaux with the full Plancherel measure.

AB - We present a sketch of the Fourier theory on the in.nite symmetric group S ∞. As a dual space to S ∞, 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 ∞, m) of square summable functions on the infinite symmetric group with the counting measure and the space L2(B,μ ̃) of square integrable functions on the groupoid of bitableaux with the full Plancherel measure.

UR - http://www.scopus.com/inward/record.url?scp=33748640593&partnerID=8YFLogxK

U2 - 10.1007/s10958-006-0334-0

DO - 10.1007/s10958-006-0334-0

M3 - Article

AN - SCOPUS:33748640593

VL - 138

SP - 5663

EP - 5673

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 3

ER -

ID: 49790052