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SUMMARY:On lower Bruhat Intervals in affine Weyl groups
DTSTART:20260924T091500Z
DTEND:20260924T101500Z
DTSTAMP:20260929T223700Z
UID:indico-event-17342@indico.math.cnrs.fr
DESCRIPTION:Speakers: Damian De La Fuente (Amiens)\n\nThe Bruhat order on 
 a Weyl group arises naturally from geometry\, through inclusion relations 
 among Schubert varieties\, but it can also be defined combinatorially in t
 he broader context of Coxeter systems. It is of major importance in Kazhda
 n-Lusztig theory\, serving to define the remarkable Kazhdan-Lusztig basis 
 and polynomials. Many fundamental questions about this partial order remai
 n open\; for instance\, the combinatorial invariance conjecture asserts th
 at Kazhdan-Lusztig polynomials are entirely determined by the poset struct
 ure of the underlying Bruhat intervals.\nIn this talk we will center on th
 e study of lower Bruhat intervals (starting from the identity) for the cas
 e of affine Weyl groups and\, specifically\, on calculating their size. Fi
 rst\, I will describe certain lower intervals by decomposing them in terms
  of lattice points in permutohedra. In turn\, we will deduce a polynomial 
 counting formula for the size of such intervals\, expressed as a linear co
 mbination of the volumes of the faces of this polytope. Secondly\, we will
  aim to generalize these results to almost all lower intervals: those aris
 ing from the lowest two-sided Kazhdan-Lusztig cell. The main object of stu
 dy will be what we call "Paper Boat" sets\, which will serve as fundamenta
 l building blocks of these lower intervals. This work is part of an on-goi
 ng collaboration with Federico Castillo\, Nicolás Libedinsky and David Pl
 aza.\n\nhttps://indico.math.cnrs.fr/event/17342/
LOCATION:L209 (Saint-Etienne)
URL:https://indico.math.cnrs.fr/event/17342/
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