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SUMMARY:Total positivity\, Schubert positivity\, and geometric Satake - La
 m\, T (Harvard)
DTSTART:20090625T130000Z
DTEND:20090625T140000Z
UID:TALK18857@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Let G be a complex simple simply-connected algebraic group. A 
 theorem proved independently by Ginzburg and Peterson states that the homo
 logy H_*(Gr_G) of the affine Grassmannian of G is isomorphic to the ring o
 f functions on the centralizer X of a principal nilpotent in the Langlands
  dual G^ee. There is a notion of total positivity on X\, using Lusztig's 
 general definitions\, and there is also a notion of Schubert positivity\, 
 using Schubert classes of Gr_G. We connect the two notions using the geome
 tric Satake correspondence. In addition\, we give an explicit parametrizat
 ion of the positive points of X. \n\nThis is joint work with Konstanze Rie
 tsch\, generalizing work of hers in type A.
LOCATION:Seminar Room 1\, Newton Institute
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