Irreducible Regular Gaussian Representations of the Groups of the Interval and Circle Diffeomorphisms

Kosyak, A. V.

doi:10.1006/jfan.1994.1135

Cited by 19 publications

(17 citation statements)

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“…In [20] Conjecture 2 was proved for the groups of the interval and circle diffeomorphisms. For the group of the interval diffeomorphisms the Shavgulidze measure [35] was used, the image of the classical Wiener measure with respect to some bijection.…”

Section: Remarkmentioning

confidence: 97%

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Quasiregular representations of the infinite-dimensional nilpotent group

Albeverio

Kosyak

2006

Journal of Functional Analysis

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In the present work an analog of the quasiregular representation which is well known for locally-compact groups is constructed for the nilpotent infinite-dimensional group B N 0 and a criterion for its irreducibility is presented. This construction uses the infinite tensor product of arbitrary Gaussian measures in the spaces R m with m > 1 extending in a rather subtle way previous work of the second author for the infinite tensor product of one-dimensional Gaussian measures.

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Section: Remarkmentioning

confidence: 97%

“…An analog of the regular representation for an arbitrary infinite-dimensional group G, using a G-quasi-invariant measure on some completion G of such a group, is defined in [18,20].…”

Section: Remarkmentioning

confidence: 99%

Quasiregular representations of the infinite-dimensional nilpotent group

Albeverio

Kosyak

2006

Journal of Functional Analysis

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“…In [25] the criterion was proved for groups of the interval and circle diffeomorphisms. For the group of the interval diffeomorphisms the Shavgulidze measure [40] was used, the image of the classical Wiener measure with respect to some bijection.…”

Section: An Analog Of the Regular And Quasiregular Representations Ofmentioning

confidence: 98%

“…An analog of the regular representation for an arbitrary infinite-dimensional group G; using a Gquasi-invariant measure on some completionG of such a group, is defined in [23,25].…”

Section: An Analog Of the Regular And Quasiregular Representations Ofmentioning

confidence: 99%

Quasiregular representations of the infinite-dimensional Borel group

Albeverio

Kosyak

2005

Journal of Functional Analysis

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“…In [4], the commutation theorem was proved for all analog of the regular representation of the current group in the case of the Wiener measure. An analog of the regular representation for an arbitrary infinite-dimensional topological group G was defined with the use of G-quasi-invariant measures # on hal appropriate completion G of G in [5,6].Consider tile group B ~ {x We shMt prove the following theorem. …”

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confidence: 99%

Inversion quasi-invariant Gaussian measures on the group of upper-triangular matrices of infinite order

Kosyak¹

2000

Funct Anal Its Appl

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519.46The following commutation theorem holds for locally compact groups [1]. The commutant of the right regular representation p of a locally compact group G is generated by the operators of the left regular representation A. Moreover, there exists an intertwining operator J such that Jpr = A~, t E G. It is given by (Jf)(x) = (dh(x-1)/dh(x))l/2f(x2i), where dh is a left Haar measure.Apparently, an analog of the regular representation for infinite-dimensional groups (current groups) appeared for the first time in [2,3]. In [4], the commutation theorem was proved for all analog of the regular representation of the current group in the case of the Wiener measure. An analog of the regular representation for an arbitrary infinite-dimensional topological group G was defined with the use of G-quasi-invariant measures # on hal appropriate completion G of G in [5,6].Consider tile group B ~ {x We shMt prove the following theorem. ~L (b~b-1 Theorem 1. /f E(b) = ~ ~k

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Irreducible Regular Gaussian Representations of the Groups of the Interval and Circle Diffeomorphisms

Cited by 19 publications

References 0 publications

Quasiregular representations of the infinite-dimensional nilpotent group

Quasiregular representations of the infinite-dimensional nilpotent group

Quasiregular representations of the infinite-dimensional Borel group

Inversion quasi-invariant Gaussian measures on the group of upper-triangular matrices of infinite order

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