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CATEGORIES:Junior Algebra and Number Theory seminar
SUMMARY:Realising The Smooth Representations of GL(2\,Zp)
- Tom Adams\, University of Cambridge
DTSTART;TZID=Europe/London:20221104T150000
DTEND;TZID=Europe/London:20221104T160000
UID:TALK192350AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/192350
DESCRIPTION:The character table of GL(2\,Fq)\, for a prime pow
er q\, was constructed over a century ago. Many of
these characters were determined via the explicit
construction of a corresponding representation\,
but purely character-theoretic techniques were fir
st used to compute the so-called discrete series c
haracters. It was not until the 1970s that Drinfel
d was able to explicitly construct the correspondi
ng discrete series representations via l-adic étal
e cohomology groups. This work was later generalis
ed by Deligne and Lusztig to all finite groups of
Lie type\, giving rise to Deligne-Lusztig theory.\
n\nIn a similar vein\, we would like to construct
the representations affording the (smooth) charact
ers of compact groups like GL(2\,Zp)\, where Zp is
the ring of p-adic integers. Deligne-Lusztig theo
ry suggests hunting for these representations insi
de certain cohomology groups. In this talk\, I wil
l consider one such approach using a non-archimede
an analogue of de Rham cohomology.\n
LOCATION:CMS MR13
CONTACT:Tom Adams
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