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 M3//EN
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METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20250313T140632Z
DTSTART:20250318T140000Z
DTEND:20250318T150000Z
SUMMARY:Algebra seminar - Tuan Pham
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}n1qb-m7em08
 l9-6aouwa
DESCRIPTION:Title: The orbit method for the Virasoro algebra\nAbstract: L
 et W = C[t\, t^{-1}]\\del_t be the Witt algebra of algebraic vector fiel
 ds on C* and let Vir be the Virasoro algebra\, the unique nontrivial cen
 tral extension of W. In [Petukhov\, Sierra 2022]\, it was shown that Poi
 sson primitive ideals of S(W) and S(Vir) can be constructed from element
 s of W* and Vir* of a particular form\, called local functions. In this 
 talk\, we show how to use a local function on W or Vir to construct a re
 presentation of the Lie algebra. We further show that the annihilators o
 f these representations are new completely prime primitive ideals of U(W
 ) and U(Vir). We use this to define a Dixmier map from the Poisson primi
 tive spectrum of S(Vir)\, respectively S(W)\, to the primitive spectrum 
 of U(Vir)\, respectively U(W)\, successfully extending the orbit method 
 from finite-dimensional solvable Lie algebras to the countable-dimension
 al setting.\n\nOur method involves new ring homomorphisms from U(W) to t
 he tensor product of a localized Weyl algebra and the enveloping algebra
  of a finite-dimensional solvable subquotient of W. We further show that
  the kernels of these homomorphisms are intersections of the primitive i
 deals constructed from natural subsets of W*.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
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