Tensor square of the basic spin representations of Schur covering groups for the symmetric groups

2020 ◽  
Author(s):  
Kazuya Aokage
Keyword(s):  
Symmetric Groups ◽  
Basic Spin ◽  
Tensor Square ◽  
Spin Representations ◽  
Covering Groups

scholarly journals The multistep homology of the simplex and representations of symmetric groups

2019 ◽  
Vol 169 (2) ◽  
pp. 231-253
Author(s):  
MARK WILDON
Keyword(s):  
Symmetric Group ◽  
Symmetric Groups ◽  
Explicit Construction ◽  
Fixed Size ◽  
Simplicial Homology ◽  
Chain Complexes ◽  
Basic Spin ◽  
Characteristic Two

AbstractThe symmetric group on a set acts transitively on the set of its subsets of a fixed size. We define homomorphisms between the corresponding permutation modules, defined over a field of characteristic two, which generalize the boundary maps from simplicial homology. The main results determine when these chain complexes are exact and when they are split exact. As a corollary we obtain a new explicit construction of the basic spin modules for the symmetric group.

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 2-Blocks of the Covering Groups of the Symmetric Groups

1997 ◽  
Vol 129 (2) ◽  
pp. 261-300 ◽  
Author(s):  
Christine Bessenrodt ◽  
Jørn B. Olsson
Keyword(s):  
Symmetric Groups ◽  
Covering Groups

On the non-abelian tensor square of groups of order p4 where p is an odd prime

ScienceAsia ◽  
2013 ◽  
Vol 39S (1) ◽  
pp. 16 ◽  
Author(s):  
Rosita Zainal ◽  
Nor Muhainiah Mohd Ali ◽  
Nor Haniza Sarmin ◽  
Samad Rashid
Keyword(s):  
Tensor Square
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