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CATEGORIES:Algebra and Representation Theory Seminar
SUMMARY:Partition algebras and Deligne's category Rep(S_t)
- Stuart Martin
DTSTART;TZID=Europe/London:20181031T163000
DTEND;TZID=Europe/London:20181031T173000
UID:TALK111691AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/111691
DESCRIPTION:A recent trend in mathematics is a renewed focus o
n the idea of\n"categorification"\, in which some
useful mathematical structure is replaced\nby a ca
tegory that models the original structure in some
way\, such that the\noriginal structure is recover
ed by taking isomorphism classes of objects.\nFor
example\, the category of Sets categorifies the na
tural numbers N. The\nnotion of monoidal category
(also known as tensor category) is a\ncategorifica
tion of monoid. Tensor categories have been studie
d since\nMacLane and others in the 1960s\, but the
re is renewed interest in them.\nIndeed\, there is
a recent book on the subject.\n\nDeligne (2007) c
onstructed a tensor category Rep(S_t)\, analogous
to the\ncategory Rep(S_n) of complex representatio
ns of the symmetric group S_n\,\nexcept that t is
allowed to be any complex number. You might ask ho
w can a\nnon-existent thing have representations?
I will try to answer this question\,\nusing combin
atorial gadgets called partition diagrams (which a
re related to\nthe partition algebra independently
discovered by V. Jones and P.P. Martin\nin the 19
90s). This talk is largely expository and I will m
ainly follow a\n2011 paper of Comes and Ostrik.\n\
n
LOCATION:MR12
CONTACT:Christopher Brookes
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