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SUMMARY:Shrawan Kumar (University of North Carolina)
DTSTART:20210723T010000Z
DTEND:20210723T023000Z
DTSTAMP:20260412T203311Z
UID:SAGO/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SAGO/6/">Roo
 t components for tensor product of affine Kac-Moody Lie algebra modules</a
 >\nby Shrawan Kumar (University of North Carolina) as part of Algebra Semi
 nar (presented by SMRI)\n\n\nAbstract\nThis is a joint work with Samuel Je
 ralds. Let gg be an affine Kac-Moody Lie algebra and let λ\, µ be two do
 minant integral weights for g. We prove that under some mild restriction\,
  for any positive root β\, V(λ) ⊗ V(µ) contains V(λ + µ - β) as a 
 component\, where V(λ) denotes the integrable highest weight (irreducible
 ) g-module with highest weight λ. This extends the corresponding result b
 y Kumar from the case of finite dimensional semisimple Lie algebras to the
  affine Kac-Moody Lie algebras. One crucial ingredient in the proof is the
  action of Virasoro algebra via the Goddard-Kent-Olive construction on the
  tensor product V(λ) ⊗ V(µ). Then\, we prove the corresponding geometr
 ic results including the higher cohomology vanishing on the G-Schubert var
 ieties in the product partial flag variety G/P × G/P with coefficients in
  certain sheaves coming from the ideal sheaves of G-sub Schubert varieties
 . This allows us to prove the surjectivity of the Gaussian map.\n
LOCATION:https://researchseminars.org/talk/SAGO/6/
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