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DTSTAMP:20250717T125353Z
DESCRIPTION:Séminaire LACIM\n\nDecompositions of Grothendieck polynomials\n
 \nOliver Pechenik\, Rutgers University\n\nSite web : http://www.lacim.uqam
 .ca\n\nAbstract: \n\nFinding a combinatorial rule for the Schubert structu
 re constants in the K-theory of flag varieties is a long-standing problem.
  The Grothendieck polynomials of Lascoux and Schützenberger (1982) serve a
 s polynomial representatives for K-theoretic Schubert classes\, but no pos
 itive rule for their multiplication is known outside the Grassmannian case
 . We contribute a new basis for polynomials\, give a positive combinatoria
 l formula for the expansion of Grothendieck polynomials in these 'glide po
 lynomials'\, and provide a positive combinatorial Littlewood-Richardson ru
 le for expanding a product of Grothendieck polynomials in the glide basis.
  A specialization of the glide basis recovers the fundamental slide polyno
 mials of Assaf and Searles (2016)\, which play an analogous role with resp
 ect to the Chow ring of flag varieties. Additionally\, the stable limits o
 f another specialization of glide polynomials are Lam and Pylyavskyy's (20
 07) basis of multi-fundamental quasisymmetric functions\, K-theoretic anal
 ogues of I. Gessel's (1984) fundamental quasisymmetric functions. Those gl
 ide polynomials that are themselves quasisymmetric are truncations of mult
 i-fundamental quasisymmetric functions and form a basis of quasisymmetric 
 polynomials. (Joint work with D. Searles).\n
DTSTART:20161202T183000Z
DTEND:20161202T183000Z
LOCATION:201\, av. du Président-Kennedy\, LOCAL PK-4323\, Montréal (Qc) H2X
  3Y7\, CA\, Pavillon Président-Kennedy
SUMMARY:Oliver Pechenik\, Rutgers University
URL:/mathstat/channels/event/oliver-pechenik-rutgers-u
 niversity-264451
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