Geodesic
Extended Gelfand--Tsetlin Graph, Its $q$-Boundary, and $q$-B-Splines
Funkcionalʹnyj analiz i ego priloženiâ, Tome 50 (2016) no. 2, pp. 31-60

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $U(\infty)$. The problem of harmonic analysis on the group $U(\infty)$ 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.
Keywords: Gelfand–Tsetlin graph, Feller property, B-splines.
Mots-clés : Markov kernels 
@article{FAA_2016_50_2_a2,
     author = {G. I. Olshanskii},
     title = {Extended {Gelfand--Tsetlin} {Graph,} {Its} $q${-Boundary,} and $q${-B-Splines}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {31--60},
     publisher = {mathdoc},
     volume = {50},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2016_50_2_a2/}
}
TY  - JOUR
AU  - G. I. Olshanskii
TI  - Extended Gelfand--Tsetlin Graph, Its $q$-Boundary, and $q$-B-Splines
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2016
SP  - 31
EP  - 60
VL  - 50
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2016_50_2_a2/
LA  - ru
ID  - FAA_2016_50_2_a2
ER  - 
%0 Journal Article
%A G. I. Olshanskii
%T Extended Gelfand--Tsetlin Graph, Its $q$-Boundary, and $q$-B-Splines
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2016
%P 31-60
%V 50
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2016_50_2_a2/
%G ru
%F FAA_2016_50_2_a2
G. I. Olshanskii. Extended Gelfand--Tsetlin Graph, Its $q$-Boundary, and $q$-B-Splines. Funkcionalʹnyj analiz i ego priloženiâ, Tome 50 (2016) no. 2, pp. 31-60. http://geodesic.mathdoc.fr/item/FAA_2016_50_2_a2/