Diagram algebras, dominance triangularity, and skew cell modules

TY - JOUR

T1 - Diagram algebras, dominance triangularity, and skew cell modules

AU - Enyang, John

AU - Goodman, Frederick

AU - Bowman-Scargill, Chris

N1 - Funding Information: We would like to thank the Royal Commission for the Exhibition of 1851 and EPSRC grant EP/L01078X/1 for financial support. Publisher Copyright: © 2017 Australian Mathematical Publishing Association Inc.

PY - 2018/2/1

Y1 - 2018/2/1

N2 - 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.

AB - 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.

KW - cellular algebras

KW - diagram algebras

UR - http://www.scopus.com/inward/record.url?scp=85032208504&partnerID=8YFLogxK

U2 - 10.1017/S1446788717000179

DO - 10.1017/S1446788717000179

M3 - Article

AN - SCOPUS:85032208504

SN - 1446-7887

VL - 104

SP - 13

EP - 36

JO - Journal of the australian mathematical society

JF - Journal of the australian mathematical society

IS - 1

ER -