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SUMMARY:Elie Casbi (MPI Bonn)
DTSTART:20201102T130000Z
DTEND:20201102T140000Z
DTSTAMP:20260710T044510Z
UID:paris-algebra-seminar/28
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/paris-algebr
 a-seminar/28/">Equivariant multiplicities of simply-laced type flag minors
 </a>\nby Elie Casbi (MPI Bonn) as part of Paris algebra seminar\n\n\nAbstr
 act\nThe study of remarkable bases of (quantum) coordinate rings has been 
 an area of\nintensive research since the early 90's. For instance\, the mu
 ltiplicative properties of \nthese bases (in particular the dual canonical
  basis) was one of the main motivations for\nthe introduction of cluster a
 lgebras by Fomin and Zelevinsky around 2000. \nIn recent work\, Baumann-Ka
 mnitzer-Knutson introduced an algebra morphism \n$\\overline{D}$ from the
  coordinate algebra $\\mathbb{C}[N]$ of a maximal unipotent subgroup $N$\n
 to the function field of a maximal torus. It is related to the geometry of
  \nMirkovic-Vilonen cycles via the notion of equivariant multiplicity. Thi
 s morphism \nturns out to be useful for comparing good bases of the coordi
 nate algebra \n$\\mathbb{C}[N]$. We will  focus on comparing the values ta
 ken by $\\overline{D}$ on several distinguished elements of the Mirkovic-V
 ilonen basis and the dual canonical basis. For the latter one\,\nwe will u
 se Kang-Kashiwara-Kim-Oh's monoidal categorification of the cluster\nstruc
 ture of the cluster structure of $\\mathbb{C}[N]$ via quiver Hecke algebra
 s as well as\nrecent results by Kashiwara-Kim. This will lead us to an exp
 licit description of\nthe images under $\\overline{D}$ of the flag minors 
 of $\\mathbb{C}[N]$ as well as remarkable\nidentities between them.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/28/
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