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SUMMARY:Partition algebras and Deligne's category Rep(S_t) - Stuart Martin
DTSTART:20181031T163000Z
DTEND:20181031T173000Z
UID:TALK111691@talks.cam.ac.uk
CONTACT:Christopher Brookes
DESCRIPTION:A recent trend in mathematics is a renewed focus on the idea o
 f\n"categorification"\, in which some useful mathematical structure is rep
 laced\nby a category that models the original structure in some way\, such
  that the\noriginal structure is recovered by taking isomorphism classes o
 f objects.\nFor example\, the category of Sets categorifies the natural nu
 mbers N. The\nnotion of monoidal category (also known as tensor category) 
 is a\ncategorification of monoid. Tensor categories have been studied sinc
 e\nMacLane and others in the 1960s\, but there is renewed interest in them
 .\nIndeed\, there is a recent book on the subject.\n\nDeligne (2007) const
 ructed a tensor category Rep(S_t)\, analogous to the\ncategory Rep(S_n) of
  complex representations of the symmetric group S_n\,\nexcept that t is al
 lowed to be any complex number. You might ask how can a\nnon-existent thin
 g have representations? I will try to answer this question\,\nusing combin
 atorial gadgets called partition diagrams (which are related to\nthe parti
 tion algebra independently discovered by V. Jones and P.P. Martin\nin the 
 1990s). This talk is largely expository and I will mainly follow a\n2011 p
 aper of Comes and Ostrik.\n\n
LOCATION:MR12
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