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SUMMARY:Multiplicities of representations of compact Lie groups\, qualitat
 ive properties and some computations - Vergne\, M (Institut de Mathmatique
 s de Jussieu)
DTSTART:20131017T103000Z
DTEND:20131017T113000Z
UID:TALK48236@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Co-author: Baldoni Velleda (Roma Tor Vergata-Italy) \n\n Let V
  be a representation space for a compact connected Lie group G decomposing
  as a sum of irreductible representations pi of G with finite multiplicity
  m(pi\,V).\n \nWhen V is constructed as the geometric quantization of a sy
 mplectic manifold with proper moment map\, the multiplicity function pi-> 
 m(pi\,V)$ is piecewise quasi polynomial on the cone of dominant weights. I
 n particular\, the function t-> m(t *pi\,V) is a quasipolynomial\,alonf th
 e ray t*pi\, when t runs over the non negative integers. We will explain h
 ow to compute effectively this quasi-polynomial (or the Duistermaat-Heckma
 n measure) in some examples\, including the function t-> c(t*lambda\,t* mu
 \,t*nu) for Clebsch-Gordan coefficients (in low rank) and the function t->
  k(t*alpha\,t*beta\,t*gamma) for Kronecker-coefficients (with number of ro
 ws less or equal to 3). Our method is based on a multidimensional residue 
 theorem (Jeffrey-Kirwan residues).\n\n
LOCATION:Seminar Room 1\, Newton Institute
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