BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Extensions of Specht modules and p-ary designs - Liam Jolliffe
DTSTART:20211124T163000Z
DTEND:20211124T173000Z
UID:TALK165049@talks.cam.ac.uk
CONTACT:Stacey Law
DESCRIPTION:The Specht modules are of fundamental importance to the repres
 entation theory of the symmetric group\, and their 0th cohomology is under
 stood through entirely combinatorial methods due to Gordon James. Over fie
 lds of odd characteristic\, Hemmer proposed a similar combinatorial approa
 ch to calculating their 1st degree cohomology\, or extensions by the trivi
 al module. This combinatorial approach motivates the definition of univers
 al p-ary designs\, which we shall classify. We then explore the consequenc
 es of this classification to problem of determining extensions of Specht m
 odules. In particular\, we classify all extensions of Specht modules index
 ed by two-part partitions by the trivial module and shall see some far-rea
 ching conditions on when the first cohomology of a Specht module is trivia
 l.  
LOCATION:MR12
END:VEVENT
END:VCALENDAR