Symmetric group blocks of small defect

James, Gordon; Mathas, Andrew

doi:10.1016/j.jalgebra.2004.04.006

Cited by 3 publications

(2 citation statements)

References 18 publications

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“…We finish this section by saying that block theory of symmetric groups and related areas have received a lot of attention recently. We refer the interested reader to the following literature for more information: [188,49,50,133,46,51,63,166,167,93,162,163,147,186,94,78,59,79,153,149,148,67,69,172]. 11.2.…”

Section: Some Other Resultsmentioning

confidence: 99%

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Representation theory of symmetric groups and related Hecke algebras

Kleshchev

2009

Bull. Amer. Math. Soc.

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Abstract. We survey some fundamental trends in representation theory of symmetric groups and related objects which became apparent in the last fifteen years. The emphasis is on connections with Lie theory via categorification. We present results on branching rules and crystal graphs, decomposition numbers and canonical bases, graded representation theory, connections with cyclotomic and affine Hecke algebras, Khovanov-Lauda-Rouquier algebras, category O, W -algebras, etc.

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Section: Some Other Resultsmentioning

confidence: 99%

“…The additional branching information provided by Theorems 11.6, 11.7 turns out very useful in applications, see for example [15,14,30,57,131,94,177,66,196,95,134].…”

Section: Some Other Resultsmentioning

confidence: 99%

Representation theory of symmetric groups and related Hecke algebras

Kleshchev

2009

Bull. Amer. Math. Soc.

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On the structure of Specht modules in the principal block of FΣ3p

Rosas

2016

Journal of Algebra

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Let F be a field of characteristic p at least 5. We study the Loewy structures of Specht modules in the principal block of F Σ 3p . We show that a Specht module in the block has Loewy length at most 4 and composition length at most 14. Furthermore, we classify which Specht modules have Loewy length 1, 2, 3, or 4, produce a Specht module having 14 composition factors, describe the second radical layer and the socle of the reducible Specht modules, and prove that if a Specht module corresponds to a partition that is p-regular and p-restricted then the head of the Specht module does not extend the socle.

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Gordon Douglas James, 1945–2020

Mathas

2022

Bulletin of London Math Soc

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It is said that every generation of mathematicians rewrites the representation theory of the symmetric groups in their own words. Gordon James literally wrote the book on the representation theory of the symmetric groups for mathematicians in the late twentieth century and early twenty-first century, putting a particular focus on representations over finite fields. He proved many of the foundational results in the field. He was one of the first to realise, and to capitalise on, the fundamental connections between the symmetric groups, the finite general linear groups, the Iwahori-Hecke algebras and the quantised Schur algebras. The James Conjecture [34] was a central focus of research in representation theory for 30 years, before finally being shown to be false 〈58〉. (Citations of the form [A] refer to Gordon James' papers, with other papers in the literature being cited as 〈B〉.)In writing this article I reached out to many colleagues. With friends, family and students alike, a common theme was the description of Gordon as being patient and kind, with many saying that he had a mischievous sense of humour. He was an incredibly sharp and gifted mathematician who knew everything there was to know about the symmetric groups and their representation theory, and he played a pivotal role in developing much of this theory. EARLY LIFEGordon was born in Newcastle-upon-Tyne on 31 December 1945, and he grew up in Polegate, near Eastbourne. Gordon's father, Douglas, was an accountant. His mother, Lily (who was known as Toni), was the head of the language department at Hailsham School in Sussex. Toni was fluent in French and German and she picked up new languages easily -a skill that skipped a generation with Gordon. Like his mother, Gordon was an excellent teacher. From a young age, Gordon was identified as being talented at 'arithmetic', so his parents sent him to Eastbourne College as a day student for secondary school from 1959 to 1963. Like many

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Symmetric group blocks of small defect

Cited by 3 publications

References 18 publications

Representation theory of symmetric groups and related Hecke algebras

Representation theory of symmetric groups and related Hecke algebras

On the structure of Specht modules in the principal block of FΣ3p

Gordon Douglas James, 1945–2020

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