BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Algebra and Representation Theory Seminar
SUMMARY:Coloured Kac-Moody algebras - Alexandre Bouayad (U
niversity of Cambridge)
DTSTART;TZID=Europe/London:20141105T163000
DTEND;TZID=Europe/London:20141105T173000
UID:TALK55507AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/55507
DESCRIPTION:I will present a new approach to deformations of a
Kac-Moody algebra g (of it universal enveloping a
lgebra U(g) more precisely) and of its modules. Th
e construction is meant to be both elementary and
systematic.\nWe will start with the easiest case\,
that is to say with the Lie algebra sl2\, by colo
uring the crystal graphs of the Verma modules of s
l2 with deformations of the natural numbers. We wi
ll explain how a given colouring defines a deforma
tion of the Verma modules of sl2. We will see how
deformed Verma modules of sl2 can generate a defor
mation of the rigid monoidal category mod(g) of g-
modules. Colourings provide in fact a classificati
on of the deformations of the category mod(g). By
Tannaka duality\, we will then obtain that colouri
ngs form a groupoid\, isomorphic to the groupoid o
f deformations of the Hopf algebra U(g). We will r
etrieve in particular the Drinfeld-Jimbo quantum a
lgebra from a colouring by q-numbers.\nColoured Ka
c-Moody algebras were originally devised by the sp
eaker to solve conjectures of Frenkel-Hernandez\,
related to the Langlands duality for quantum group
s. We will see that two isogenic coloured Kac-Mood
y algebras can be interpolated by a third coloured
Kac-Moody algebra\, implying in particular a solu
tion to the conjectures. We will also discuss the
existence of a potential link between coloured Kac
-Moody algebras and quiver Hecke algebras of Khova
nov-Lauda-Rouquier. This may pave the way to a cat
egorification and to a geometric realisation of co
loured Kac-Moody algebras\, with eventual connecti
ons to the geometric Langlands correspondence. We
will lastly evoke other possible applications of c
oloured Kac-Moody algebras
LOCATION:MR12
CONTACT:David Stewart
END:VEVENT
END:VCALENDAR