Extended Gelfand–Tsetlin graph, its q-boundary, and q-B-splines

The boundary of the Gelfand–Tsetlin graph is an infinite-dimensional locally compact space whose points parameterize the extreme characters of the infinite-dimensional group U (∞). The problem of harmonic analysis on the group U (∞) leads to a continuous family of probability measures on the boundar...

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Bibliographic Details
Published in:Functional analysis and its applications 2016-04, Vol.50 (2), p.107-130
Main Author: Olshanski, G. I.
Format: Article
Language:English
Subjects:
Analysis
Functional Analysis
Mathematics
Mathematics and Statistics
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Summary:The boundary of the Gelfand–Tsetlin graph is an infinite-dimensional locally compact space whose points parameterize the extreme characters of the infinite-dimensional group U (∞). The problem of harmonic analysis on the group U (∞) leads to a continuous family of probability measures on the boundary—the so-called zw-measures. Recently Vadim Gorin and the author have begun to study a q -analogue of the zw-measures. It turned out that constructing them requires introducing a novel combinatorial object, the extended Gelfand–Tsetlin graph. In the present paper it is proved that the Markov kernels connected with the extended Gelfand–Tsetlin graph and its q -boundary possess the Feller property. This property is needed for constructing a Markov dynamics on the q -boundary. A connection with the B-splines and their q -analogues is also discussed.
ISSN:0016-2663
1573-8485
DOI:10.1007/s10688-016-0136-1