Projective representations of the infinite symmetric group

1992 ◽  
pp. 115-130 ◽  
Author(s):  
M. Nazarov
Keyword(s):  
Symmetric Group ◽  
Infinite Symmetric Group ◽  
Projective Representations

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.

Some combinatorial results involving shifted Young diagrams

1986 ◽  
Vol 99 (1) ◽  
pp. 23-31 ◽  
Author(s):  
A. O. Morris ◽  
A. K. Yaseen
Keyword(s):  
Symmetric Group ◽  
Block Structure ◽  
Young Diagrams ◽  
Linear Representations ◽  
Projective Representations

In [6] the first author introduced some combinatorial concepts involving Young diagrams corresponding to partitions with distinct parts and applied them to the projective representations of the symmetric group Sn. A conjecture concerning the p-block structure of the projective representations of Sn was formulated in terms of these concepts which corresponds to the well-known, but long proved, Nakayama ‘conjecture’ for the p-block structure of the linear representations of Sn. This conjecture has recently been proved by Humphreys [1].

Sign in / Sign up

Export Citation Format

Share Document