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SUMMARY:Mikhail Mazin (Kansas State University)
DTSTART:20200928T180000Z
DTEND:20200928T190000Z
DTSTAMP:20260423T021530Z
UID:UMassRep/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UMassRep/6/"
 >Equivariant K-theory of the partial flag varieties.</a>\nby Mikhail Mazin
  (Kansas State University) as part of UMass Amherst Representation theory 
 seminar\n\n\nAbstract\nBack in 1990 Beilinson\, Lusztig\, and MacPherson u
 sed convolution algebras of diagonal orbits in the double partial flag var
 ieties over finite fields to provide a geometric framework for the quantum
  groups in type A. In 1998 Vasserot used equivariant K-theory of the Stein
 berg subvarieties in the cotangent bundle of the double partial flag varie
 ties to provide a geometric framework for the affine quantum group.\n\nIn 
 a joint project with Sergey Arkhipov\, we define an algebra $\\mathcal{A}_
 n$ that plays the role of a $q=0$ degeneration of the affine quantum group
  of type $A_n$\, and use the equivariant K-theory of the double partial fl
 ag variety with $n$ steps to provide a geometric framework for it. Our alg
 ebra is defined via generators and relations. Then for each dimension $d$ 
 of the ambient space\, we show that there is a natural surjective map $\\m
 athcal{A}_n\\to A(n\,d)$\, were $A(n\,d)$ is the equivariant K-theory of t
 he double partial flag variety  with n step in $\\mathbb{C}^d$ equipped wi
 th the convolution product.\n
LOCATION:https://researchseminars.org/talk/UMassRep/6/
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