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Lie Group Quantum Mathematics Seminar

Strong integrality of inversion subgroups of Kac-Moody groups

Abid Ali, Rutgers University

Location:  Hill Center Room 705
Date & time: Friday, 09 December 2022 at 12:10PM - 1:10PM

Abstract Let g be a symmetrizable Kac-Moody algebra over Q. Let V be an integrable highest weight g-module and let V_Z be a Z-form of V. Let G(Q) be an associated minimal representation-theoretic Kac-Moody group and let G(Z) be its integral subgroup. Let Gamma(Z) be the Chevalley subgroup of G, that is, the subgroup that stabilizes the lattice V_Z in V. It is a difficult question to determine if G(Z)=Gamma(Z). We establish this equality for inversion subgroups U_w of G where, for an element w of the Weyl group, U_w is the group generated by positive real root groups that are flipped to negative roots by w^{-1}. This result extends to other subgroups of G, particularly when G has rank 2. This is joint work with Lisa Carbone, Dongwen Liu and Scott H. Murray.
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