A panorama of diagram algebras

2009 ◽  
pp. 491-540 ◽  
Author(s):  
Steffen Koenig
Keyword(s):  
Diagram Algebras

scholarly journals Constructing cell data for diagram algebras

2007 ◽  
Vol 209 (2) ◽  
pp. 551-569 ◽  
Author(s):  
R.M. Green ◽  
P.P. Martin
Keyword(s):  
Diagram Algebras ◽  
Cell Data

scholarly journals Towers of recollement and bases for diagram algebras: Planar diagrams and a little beyond

2007 ◽  
Vol 316 (1) ◽  
pp. 392-452 ◽  
Author(s):  
Paul Martin ◽  
R.M. Green ◽  
Alison Parker
Keyword(s):  
Diagram Algebras

THE KLEIN-4 DIAGRAM ALGEBRAS

2008 ◽  
Vol 07 (02) ◽  
pp. 231-262
Author(s):  
M. PARVATHI ◽  
B. SIVAKUMAR
Keyword(s):  
Bratteli Diagram ◽  
Permutation Representation ◽  
Signed Permutation ◽  
Permutation Module ◽  
New Class ◽  
Diagram Algebras ◽  
Irreducible Modules ◽  
Centralizer Algebras ◽  
Partition Algebras ◽  
Tensor Powers

In this paper we study a new class of diagram algebras, the Klein-4 diagram algebras denoted by Rk(n). These algebras are the centralizer algebras of the group Gn := (ℤ2 × ℤ2)≀Sn acting on V⊗k, where V is the signed permutation module for Gn These algebras have been realized as subalgebras of the extended G-vertex colored partition algebras introduced by Parvathi and Kennedy in [7]. In this paper we give a combinatorial rule for the decomposition of the tensor powers of the signed permutation representation of Gn by explicitly constructing the basis for the irreducible modules. In the process we also give the basis for the irreducible modules appearing in the decomposition of V⊗k in [5]. We then use this rule to describe the Bratteli diagram of Klein-4 diagram algebras.

scholarly journals DIAGRAM ALGEBRAS, DOMINANCE TRIANGULARITY AND SKEW CELL MODULES

2017 ◽  
Vol 104 (1) ◽  
pp. 13-36 ◽  
Author(s):  
CHRISTOPHER BOWMAN ◽  
JOHN ENYANG ◽  
FREDERICK GOODMAN
Keyword(s):  
Transition Matrix ◽  
Hecke Algebras ◽  
Symmetric Groups ◽  
Specht Modules ◽  
Diagram Algebras ◽  
Cell Modules ◽  
Abstract Framework

We present an abstract framework for the axiomatic study of diagram algebras. Algebras that fit this framework possess analogues of both the Murphy and seminormal bases of the Hecke algebras of the symmetric groups. We show that the transition matrix between these bases is dominance unitriangular. We construct analogues of the skew Specht modules in this setting. This allows us to propose a natural tableaux theoretic framework in which to study the infamous Kronecker problem.

scholarly journals Cohomological stratification of diagram algebras

2009 ◽  
Vol 347 (4) ◽  
pp. 765-804 ◽  
Author(s):  
Robert Hartmann ◽  
Anne Henke ◽  
Steffen Koenig ◽  
Rowena Paget
Keyword(s):  
Diagram Algebras

Strong module diagrams and frobenius diagram algebras

1989 ◽  
Vol 17 (2) ◽  
pp. 259-298 ◽  
Author(s):  
Kent R. Fuller ◽  
Koichiro Ohtake
Keyword(s):  
Diagram Algebras

scholarly journals Set-partition tableaux and representations of diagram algebras

2020 ◽  
Vol 3 (2) ◽  
pp. 509-538
Author(s):  
Tom Halverson ◽  
Theodore N. Jacobson
Keyword(s):  
Set Partition ◽  
Diagram Algebras
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