SMS scnews item created by Hannah Bryant at Thu 8 Jul 2021 1703
Type: Seminar
Modified: Thu 8 Jul 2021 1710; Thu 8 Jul 2021 1711
Distribution: World
Expiry: 8 Jul 2022
Calendar1: 23 Jul 2021 1100-1230
CalLoc1: Online via Zoom
CalTitle1: SMRI Algebra and Geometry Online: Kumar -- Root components for tensor product of affine Kac-Moody Lie algebra modules
Auth: hannahb@10.48.16.40 (hbry8683) in SMS-SAML

# SMRI Algebra and Geometry Online: Kumar -- Root components for tensor product of affine Kac-Moody Lie algebra modulesâ€™

SMRI Algebra and Geometry Online
’Root components for tensor product of affine Kac-Moody Lie algebra modules’
Shrawan Kumar (University of North Carolina)

Friday Jul 23, 2021
11:00am-12:30pm (AEST)
Register:
https://uni-sydney.zoom.us/meeting/register/tZ0sc--qrzkpHdd5eE6IgQUYtXWfnEssOCIC

This is a joint work with Samuel Jeralds.  Let ð”¤ be an affine Kac-Moody Lie algebra
and let Î», Âµ be two dominant integral weights for ð”¤.  We prove that under some mild
restriction, for any positive root Î², V(Î») âŠ— V(Âµ) contains V(Î» + Âµ â€“ Î²) as a
component, where V(Î») denotes the integrable highest weight (irreducible) ð”¤-module
with highest weight Î».  This extends the corresponding result by 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(Î») âŠ— V(Âµ).  Then, we prove
the corresponding geometric results including the higher cohomology vanishing on the
ð’¢-Schubert varieties in the product partial flag variety ð’¢/ð’« Ã— ð’¢/ð’« with
coefficients in certain sheaves coming from the ideal sheaves of ð’¢-sub Schubert
varieties.  This allows us to prove the surjectivity of the Gaussian map.

Note: These seminars will be recorded, including participant questions (participants