scholarly journals On Cartan matrices and lower defect groups for covering groups of symmetric groups

2005 ◽  
Vol 358 (8) ◽  
pp. 3623-3635 ◽  
Author(s):  
Christine Bessenrodt ◽  
Jørn B. Olsson
Keyword(s):  
Symmetric Groups ◽  
Defect Groups ◽  
Cartan Matrices ◽  
Covering Groups

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

scholarly journals Lower defect groups in symmetric groups

1986 ◽  
Vol 104 (1) ◽  
pp. 37-56 ◽  
Author(s):  
Jørn B Olsson
Keyword(s):  
Symmetric Groups ◽  
Defect Groups

A note on Cartan matrices for symmetric groups

2003 ◽  
Vol 81 (5) ◽  
pp. 497-504 ◽  
Author(s):  
C. Bessenrodt ◽  
J. B. Olsson
Keyword(s):  
Symmetric Groups ◽  
Cartan Matrices

GRADED CARTAN MATRICES OF DEFECT 2 BLOCKS OF SYMMETRIC GROUPS

2013 ◽  
Vol 12 (05) ◽  
pp. 1250220
Author(s):  
DUSKO BOGDANIC
Keyword(s):  
Symmetric Groups ◽  
Decomposition Numbers ◽  
Cartan Matrices

In this paper we show how the LLT algorithm for computation of crystal decomposition numbers can be used to construct quivers of defect 2 blocks of symmetric groups. We do this by establishing a connection between tight gradings on blocks of symmetric groups and crystal decomposition numbers.

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