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UID:7164@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20181213T140000
DTEND;TZID=Europe/Paris:20181213T150000
DTSTAMP:20241120T203437Z
URL:https://www.i2m.univ-amu.fr/evenements/dirac-induction-for-hecke-algeb
 ras/
SUMMARY: (...): Dirac induction for Hecke algebras
DESCRIPTION:: The Dirac operator for graded affine Hecke algebras  was intr
 oduced by Barbasch\, Ciubotaru and Trapa (2010). Based on this constructio
 n we defined Dirac induction for graded affine Hecke algebras (Ciubotaru-O
 .-Trapa). Using this\, we (Ciubotaru-O.) showed that given a so-called "ma
 ssive" elliptic character chi of Euler-Poincare norm 1 of an affine Weyl g
 roup\, there exists a unique family Ind_D(chi) of virtual "generically dis
 crete series" characters of the associated affine Hecke algebra over its s
 pace of Hecke algebra parameters\, characterised by the property that its 
 limit for q tends to 1 has elliptic class chi. For every specialisation of
  the Hecke algebra at a positive parameter\, all its irreducible discrete 
 series characters belong to such a unique parameter family of this type.-W
 e show that the formal degree of Ind_D(chi) is a rational function m_\\chi
 (q):=fdeg(Ind_D(chi\,q)) of the Hecke parameters q\, which is regular for 
 positive parameters (this is quite striking\, because the family itself is
  not continuous). This fact enables us to compute m_\\chi(q) for every chi
  as above completely explicitly. We show that Ind_D(chi\,q) is a discrete 
 series character (up to a sign) iff m_chi(q) is nonzero\, which gives a cl
 assification of the discrete series which is uniform in the Hecke algebra 
 parameters q.-Based on joint work with Ciubotaru and Trapa (JIMJ 2014)\, a
 nd with Ciubotaru (ANT 2017). http://staff.fnwi.uva.nl/e.m.opdam/
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