Geodesic
$C$-algebras and algebras in Plancherel duality
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part II, Tome 240 (1997), pp. 53-66

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

For an arbitrary $C$-algebra (possibly non-commutative) a positivity condition generalizing the Krein condition for a commutative case is defined. We show that the class of positive $C$-algebras includes those arising in algebraic combinatorics from association schemes (possibly non-commutative). It is proved that the category of positive $C$-algebras is equivalent to the category of pairs of algebras in Plancherel duality one of which being commutative. 
@article{ZNSL_1997_240_a3,
     author = {A. M. Vershik and S. A. Evdokimov and I. N. Ponomarenko},
     title = {$C$-algebras and algebras in {Plancherel} duality},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {53--66},
     publisher = {mathdoc},
     volume = {240},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_240_a3/}
}
TY  - JOUR
AU  - A. M. Vershik
AU  - S. A. Evdokimov
AU  - I. N. Ponomarenko
TI  - $C$-algebras and algebras in Plancherel duality
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1997
SP  - 53
EP  - 66
VL  - 240
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1997_240_a3/
LA  - ru
ID  - ZNSL_1997_240_a3
ER  - 
%0 Journal Article
%A A. M. Vershik
%A S. A. Evdokimov
%A I. N. Ponomarenko
%T $C$-algebras and algebras in Plancherel duality
%J Zapiski Nauchnykh Seminarov POMI
%D 1997
%P 53-66
%V 240
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_1997_240_a3/
%G ru
%F ZNSL_1997_240_a3
A. M. Vershik; S. A. Evdokimov; I. N. Ponomarenko. $C$-algebras and algebras in Plancherel duality. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part II, Tome 240 (1997), pp. 53-66. http://geodesic.mathdoc.fr/item/ZNSL_1997_240_a3/