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SUMMARY:Affine Kazhdan-Lusztig R-polynomials for Kac-Moody groups
DTSTART:20260427T120000Z
DTEND:20260427T130000Z
DTSTAMP:20260501T113800Z
UID:indico-event-5816@agenda.irmp.ucl.ac.be
DESCRIPTION:Speakers: Paul Philippe (Universität Münster)\n\nTo any redu
 ctive group G (such as SLn) one can associate an affine flag variety X
 \, whose geometry is related to the representation theory of G and of it
 s loop group G[t\,t−1]. Kazhdan-Lusztig R-polynomials relate some of th
 e structure of X to the combinatorics of a Coxeter group associated to 
 G\, namely its affine Weyl group. These polynomials are a cornerstone in t
 he famous affine Kazhdan-Lusztig theory. If we try to replace G by a Kac
 -Moody\, non-reductive group\, X can still be defined\, but has no reaso
 nable topology\, and some of its structure is lost: there is an analog W+
  of the affine Weyl group\, but which is only a semi-group\, and has no p
 roper Coxeter structure. However in 2016 Braverman Kazhdan and Patnaik hav
 e introduced a partial order on W+ which could play the role of the Bruh
 at order. Since then\, some key combinatorial properties of this semi-grou
 p have been obtained\, making the definition of affine Kazhdan-Lusztig R-p
 olynomials in this context reasonable.In my talk\, after introducing these
  polynomials in the reductive setting\, I will present a path model constr
 uction for affine Kazhdan-Lusztig R polynomials associated to Kac-Moody gr
 oups. This path model was schemed in a prepublication of Muthiah in 2019\,
  and relies on later work of Bardy-Panse\, Hébert and Rousseau on twin ma
 sures\, which we will use as a black box. This is a joint work with A. Hé
 bert.\n\nhttps://agenda.irmp.ucl.ac.be/event/5816/
LOCATION:B/2nd floor-B.203 - Seminar room (Marc de Hemptinne (chemin du Cy
 clotron\, 2\, Louvain-la-Neuve))
URL:https://agenda.irmp.ucl.ac.be/event/5816/
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