scholarly journals Irreducible projective representations of the symmetric group which remain irreducible in characteristic 2

2017 ◽  
Vol 116 (4) ◽  
pp. 878-928 ◽  
Author(s):  
Matthew Fayers
Keyword(s):  
Symmetric Group ◽  
Projective Representations ◽  
Characteristic 2

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].

Fischer Matrices for Projective Representations of Generalized Symmetric Groups

2009 ◽  
Vol 16 (03) ◽  
pp. 449-462
Author(s):  
Mohammed S. Almestady ◽  
Alun O. Morris
Keyword(s):  
Symmetric Group ◽  
Weyl Group ◽  
Symmetric Groups ◽  
Type B ◽  
Projective Representations ◽  
Ordinary Case ◽  
Covering Groups

The aim of this work is to calculate the Fischer matrices for the covering groups of the Weyl group of type Bn and the generalized symmetric group. It is shown that the Fischer matrices are the same as those in the ordinary case for the classes of Sn which correspond to partitions with all parts odd. For the classes of Sn which correspond to partitions in which no part is repeated more than m times, the Fischer matrices are shown to be different from the ordinary case.

scholarly journals The α-regular classes of the generalized symmetric group

1976 ◽  
Vol 17 (2) ◽  
pp. 144-150 ◽  
Author(s):  
E. W. Read
Keyword(s):  
Finite Group ◽  
Symmetric Group ◽  
Analogous Problem ◽  
Normal Subgroups ◽  
Projective Representations ◽  
Regular Classes ◽  
Factor Set

The α-regular classes of any finite group G are important since they are those classes on which the projective characters of G with factor set α take non-zero value, and thus a knowledge of the α-regular classes gives the number of irreducible projective representations of G with factor set α (see [4]). Here we look at the particular case of the generalized symmetric group Cm wr Sl. The analogous problem of constructing the irreducible projective representations of Cm wr Sl has been dealt with in [6] by generalizing Clifford's theory of inducing from normal subgroups, but unfortunately, it is not in general possible to determine the irreducible projective characters (and hence the α-regular classes) by this method.

scholarly journals On the Structure of the Tensor Square of the Natural Module of the Symmetric Group

2011 ◽  
Vol 18 (04) ◽  
pp. 589-610 ◽  
Author(s):  
Jürgen Müller ◽  
Johannes Orlob
Keyword(s):  
Symmetric Group ◽  
Prime Characteristic ◽  
Characteristic 2 ◽  
Natural Module ◽  
Tensor Square

We determine the submodule structure of the tensor square of the natural module of the symmetric group over a field of prime characteristic. We also determine the submodule structure of certain Young modules over a field of characteristic 2.

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