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

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6 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)107-130
Number of pages24
JournalFunctional Analysis and its Applications
Issue number2
Publication statusPublished - 1 Apr 2016
Externally publishedYes


  • B-splines
  • Feller property
  • Gelfand–Tsetlin graph
  • Markov kernels


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