Hua measures on the space of $ p$-adic matrices and inverse limits of Grassmannians

Neretin, Yury A.

doi:10.1070/im2013v077n05abeh002665

Cited by 17 publications

(23 citation statements)

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“…Remark. The group GL(∞, O p ) appears in the context of [11]. However, GL(∞, O p ) is a more interesting object from a point of view of [12].…”

Section: The Statementmentioning

confidence: 99%

On the Group of Infinite p-Adic Matrices with Integer Elements

Neretin

2019

J Math Sci

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Let G be an infinite-dimensional real classical group containing the complete unitary group (or complete orthogonal group) as a subgroup. Then G generates a category of double cosets (train) and any unitary representation of G can be canonically extended to the train. We prove a technical lemma about the complete group GL of infinite p-adic matrices with integer coefficients, this lemma implies that the phenomenon of automatic extension of unitary representations to trains is valid for infinite-dimensional p-adic groups.

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“…Remark. The group GL(∞, O p ) appears in the context of [11]. However, GL(∞, O p ) is a more interesting object from a point of view of [12].…”

Section: The Statementmentioning

confidence: 99%

On the Group of Infinite p-Adic Matrices with Integer Elements

Neretin

2019

J Math Sci

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“…For any , we fix a Haar measure on normalized by . Up to a multiplicative constant, the Haar measure on the locally compact group is uniquely given (see, e.g., Neretin [Ner13]) by …”

Section: Preliminariesmentioning

confidence: 99%

Ergodic measures on spaces of infinite matrices over non-Archimedean locally compact fields

Bufetov

Qiu

2017

Compositio Math.

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“…1) The construction of inverse limits does not admit an extension to non-compact symmetric spaces (i.e., to matrix balls). Of course, the chain of projections of sets 2) Projective limits exist for p-adic Grassmannians, see [23].…”

Section: The Hua Integralsmentioning

confidence: 99%