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SUMMARY:Plethysms: permutations\, polynomial representations and Schur fun
 ctions - Mark Wildon (Royal Holloway)
DTSTART:20170301T163000Z
DTEND:20170301T173000Z
UID:TALK70389@talks.cam.ac.uk
CONTACT:Christopher Brookes
DESCRIPTION:The symmetric group S_mn acts on set partitions of a set of si
 ze mn into n\nsets each of size m. The character of this module is the sub
 ject of the\nlong-standing Foulkes Conjecture. It corresponds to the repre
 sentation\nSym^n^ (Sym^m^ (V)) of the infinite general linear group GL(V)\
 , obtained by\ncomposing the two symmetric-power functors\, and to the ple
 thystic product of\nthe Schur functions s_(n) and s_(m). Decomposing an ar
 bitrary plethysm into\nSchur functions has been identified by Richard Stan
 ley as a key open problem\nin algebraic combinatorics. In this overview ta
 lk I will give a\ncombinatorial description of all maximal and minimal par
 titions in the\ndominance order that label the Schur functions appearing i
 n an arbitrary\nplethysm. If time permits I will also discuss relationship
 s between plethysm\ncoefficients\, and how these may be proved via highest
 -weight vectors. This\ntalk is on joint work with Rowena Paget.\n
LOCATION:MR12
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