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SUMMARY:How to construct a rigid analytic quantum sl_2 - Nicolas Dupré\, 
 University of Cambridge
DTSTART:20151016T140000Z
DTEND:20151016T150000Z
UID:TALK61808@talks.cam.ac.uk
CONTACT:Nicolas Dupré
DESCRIPTION:Quantum groups are deformations of classical algebras such as 
 enveloping algebras of Lie algebras or coordinate rings of algebraic group
 s. A common theme about these objects is that they should still share simi
 lar properties as their classical counterparts\, and so for instance in th
 e right context we can think of quantum groups as algebras of "polynomial"
  functions on some "quantum space". When working over p-adic fields\, ther
 e is a very natural notion of (locally) analytic functions and one can def
 ine a so-called rigid analytic space\, which is essentially a space whose 
 functions are locally analytic. Therefore one can ask whether there is a g
 ood notion of algebras of analytic functions on a "quantum p-adic space"\,
  or said differently a notion of rigid analytic quantum group. We will sho
 w how to construct an analytic version of the quantized enveloping algebra
  of sl_2\, and we will then describe some of the properties that this alge
 bra satisfies which make its representation theory possible to study.
LOCATION:CMS\, MR15
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