scholarly journals An introduction to harmonic analysis on the infinite symmetric group

2007 ◽  
pp. 127-160 ◽  
Author(s):  
Grigori Olshanski
Keyword(s):  
Symmetric Group ◽  
Harmonic Analysis ◽  
Infinite Symmetric Group

scholarly journals Harmonic Functions on Multiplicative Graphs and Interpolation Polynomials

10.37236/1506 ◽  
2000 ◽  
Vol 7 (1) ◽  
Author(s):  
Alexei Borodin ◽  
Grigori Olshanski
Keyword(s):  
Symmetric Group ◽  
Harmonic Analysis ◽  
Harmonic Functions ◽  
Symmetric Functions ◽  
Multivariate Interpolation ◽  
Infinite Symmetric Group ◽  
Interpolation Polynomials

We construct examples of nonnegative harmonic functions on certain graded graphs: the Young lattice and its generalizations. Such functions first emerged in harmonic analysis on the infinite symmetric group. Our method relies on multivariate interpolation polynomials associated with Schur's S and P functions and with Jack symmetric functions. As a by–product, we compute certain Selberg–type integrals.

scholarly journals Harmonic analysis on the infinite symmetric group

2004 ◽  
Vol 158 (3) ◽  
pp. 551-642 ◽  
Author(s):  
Sergei Kerov ◽  
Grigori Olshanski ◽  
Anatoly Vershik
Keyword(s):  
Symmetric Group ◽  
Harmonic Analysis ◽  
Infinite Symmetric Group

scholarly journals Certain unitary representations of the infinite symmetric group, II

1987 ◽  
Vol 106 ◽  
pp. 143-162 ◽  
Author(s):  
Nobuaki Obata
Keyword(s):  
Symmetric Group ◽  
Discrete Group ◽  
Inductive Limit ◽  
Symmetric Groups ◽  
Discrete Groups ◽  
Type I ◽  
Infinite Symmetric Group ◽  
Locally Finite ◽  
Distinctive Features ◽  
Infinite Dimensional

The infinite symmetric group is the discrete group of all finite permutations of the set X of all natural numbers. Among discrete groups, it has distinctive features from the viewpoint of representation theory and harmonic analysis. First, it is one of the most typical ICC-groups as well as free groups and known to be a group of non-type I. Secondly, it is a locally finite group, namely, the inductive limit of usual symmetric groups . Furthermore it is contained in infinite dimensional classical groups GL(ξ), O(ξ) and U(ξ) and their representation theories are related each other.

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