Geodesic
A functional realization of the Gelfand--Tsetlin base
Izvestiya. Mathematics , Tome 87 (2023) no. 6, pp. 1117-1147

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

A realization of a finite dimensional irreducible representation of the Lie algebra $\mathfrak{gl}_n$ in the space of functions on the group $\mathrm{GL}_n$ is considered. It is proved that functions corresponding to Gelfand–Tsetlin diagrams are linear combinations of some new functions of hypergeometric type which are closely related to $A$-hypergeometric functions. These new functions are solution of a system of partial differential equations which follows from the Gelfand–Kapranov–Zelevinsky by an “antisymmetrization”. The coefficients in the constructed linear combination are hypergeometric constants, that is, they are values of some hypergeometric functions when instead of all arguments ones are substituted.
Keywords: the Gelfand–Tsetlin base, hypergeometric functions, the Gelfand–Kapranov–Zelevinsky system. 
@article{IM2_2023_87_6_a0,
     author = {D. V. Artamonov},
     title = {A functional realization of the {Gelfand--Tsetlin} base},
     journal = {Izvestiya. Mathematics },
     pages = {1117--1147},
     publisher = {mathdoc},
     volume = {87},
     number = {6},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2023_87_6_a0/}
}
TY  - JOUR
AU  - D. V. Artamonov
TI  - A functional realization of the Gelfand--Tsetlin base
JO  - Izvestiya. Mathematics 
PY  - 2023
SP  - 1117
EP  - 1147
VL  - 87
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2023_87_6_a0/
LA  - en
ID  - IM2_2023_87_6_a0
ER  - 
%0 Journal Article
%A D. V. Artamonov
%T A functional realization of the Gelfand--Tsetlin base
%J Izvestiya. Mathematics 
%D 2023
%P 1117-1147
%V 87
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2023_87_6_a0/
%G en
%F IM2_2023_87_6_a0
D. V. Artamonov. A functional realization of the Gelfand--Tsetlin base. Izvestiya. Mathematics , Tome 87 (2023) no. 6, pp. 1117-1147. http://geodesic.mathdoc.fr/item/IM2_2023_87_6_a0/