Specht Modules of Trivial Source and the Endomorphism Ring of the Lie Module

The source of a Specht module is not generally known, unless it is a projective or irreducible module and in this case the source is trivial. Are these the only Specht modules with trivial source? To address this question, we classify the Specht modules of FΣ2p and FΣ2p+1 with trivial source for p≥3. It turns out that a Specht module of FΣ2p and FΣ2p+1 corresponding to a weight two partition has trivial source if and only if it is irreducible. On the other hand, there are Specht modules corresponding to weight one partitions that are not irreducible but have trivial source, these can be identified by ordering the partitions (using the lexicographic ordering) in the block to which they belong. The result concerning Specht modules corresponding to weight one partitions with trivial source is not unique to FΣ2p and FΣ2p+1 , but it generalizes to Specht modules of FΣn for any 5≤p≤n.

Grantor dc:publisher

State University of New York at Buffalo

Year dc:date.issued

2018

Author dc:creator

• Hudson, Tara

Contributors dc:contributor

• Hemmer, David
• Mathematics

• mathematics

Statement dc:rights

• Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.
• Copyright retained by author.

Language dc:language

eng

Handle dc:identifier

http://hdl.handle.net/10477/78037

OAI record oai:identifier

https://ubir.buffalo.edu/oai/request?verb=GetRecord&metadataPrefix=qdc&identifier=oai%3Aubir.buffalo.edu%3A10477%2F78037