scholarly journals Cellularity of signed symmetric group algebras

2020 ◽  
Author(s):  
R. Venkatesan ◽  
E. Nandakumar ◽  
Gaverchand K.
Keyword(s):  
Symmetric Group ◽  
Group Algebras ◽  
Symmetric Group Algebras

scholarly journals Defect 3 Blocks of Symmetric Group Algebras, I

2001 ◽  
Vol 237 (1) ◽  
pp. 95-120 ◽  
Author(s):  
Stuart Martin ◽  
Kai Meng Tan
Keyword(s):  
Symmetric Group ◽  
Group Algebras ◽  
Symmetric Group Algebras

scholarly journals On the Ext-Quiver of Blocks of Defect 3 of Symmetric Group Algebras

1996 ◽  
Vol 185 (2) ◽  
pp. 440-480 ◽  
Author(s):  
Stuart Martin ◽  
Lee Russell
Keyword(s):  
Symmetric Group ◽  
Group Algebras ◽  
Symmetric Group Algebras

scholarly journals The center of the wreath product of symmetric group algebras

2021 ◽  
Vol 31 (2) ◽  
pp. 302-322
Author(s):  
O. Tout ◽  
Keyword(s):  
Symmetric Group ◽  
Recent Result ◽  
Wreath Product ◽  
Group Algebra ◽  
Symmetric Groups ◽  
Conjugacy Classes ◽  
Group Algebras ◽  
Hyperoctahedral Group ◽  
Symmetric Group Algebras

We consider the wreath product of two symmetric groups as a group of blocks permutations and we study its conjugacy classes. We give a polynomiality property for the structure coefficients of the center of the wreath product of symmetric group algebras. This allows us to recover an old result of Farahat and Higman about the polynomiality of the structure coefficients of the center of the symmetric group algebra and to generalize our recent result about the polynomiality property of the structure coefficients of the center of the hyperoctahedral group algebra.

scholarly journals On Young Modules of Defect 2 Blocks of Symmetric Group Algebras

1999 ◽  
Vol 221 (2) ◽  
pp. 651-668 ◽  
Author(s):  
Joseph Chuang ◽  
Kai Meng Tan
Keyword(s):  
Symmetric Group ◽  
Group Algebras ◽  
Symmetric Group Algebras

scholarly journals RSK Insertion for Set Partitions and Diagram Algebras

10.37236/1881 ◽  
2005 ◽  
Vol 11 (2) ◽  
Author(s):  
Tom Halverson ◽  
Tim Lewandowski
Keyword(s):  
Representation Theory ◽  
Symmetric Group ◽  
Group Algebras ◽  
Jeu De Taquin ◽  
Set Partitions ◽  
Partition Algebra ◽  
Diagram Algebras ◽  
Rook Monoid ◽  
Planar Partition ◽  
Symmetric Group Algebras

We give combinatorial proofs of two identities from the representation theory of the partition algebra ${\Bbb C} A_k(n)$, $n \ge 2k$. The first is $n^k = \sum_\lambda f^\lambda m_k^\lambda$, where the sum is over partitions $\lambda$ of $n$, $f^\lambda$ is the number of standard tableaux of shape $\lambda$, and $m_k^\lambda$ is the number of "vacillating tableaux" of shape $\lambda$ and length $2k$. Our proof uses a combination of Robinson-Schensted-Knuth insertion and jeu de taquin. The second identity is $B(2k) = \sum_\lambda (m_k^\lambda)^2$, where $B(2k)$ is the number of set partitions of $\{1, \ldots, 2k\}$. We show that this insertion restricts to work for the diagram algebras which appear as subalgebras of the partition algebra: the Brauer, Temperley-Lieb, planar partition, rook monoid, planar rook monoid, and symmetric group algebras.

scholarly journals Free symmetric group algebras in division rings generated by poly-orderable groups

2013 ◽  
Vol 392 ◽  
pp. 69-84 ◽  
Author(s):  
Vitor O. Ferreira ◽  
Jairo Z. Gonçalves ◽  
Javier Sánchez
Keyword(s):  
Symmetric Group ◽  
Group Algebras ◽  
Division Rings ◽  
Symmetric Group Algebras
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