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SUMMARY:Abid Ali (University of Saskatchewan)
DTSTART:20231012T223000Z
DTEND:20231013T000000Z
DTSTAMP:20260423T005651Z
UID:PIMS_GAP/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PIMS_GAP/15/
 ">Strong integrality of inversion subgroups of Kac-Moody groups</a>\nby Ab
 id Ali (University of Saskatchewan) as part of PIMS Geometry / Algebra / P
 hysics (GAP) Seminar\n\nLecture held in THORV 124.\n\nAbstract\nThe questi
 on of integrality for semi-simple algebraic groups over the field of ratio
 nal numbers was established by Chevalley in the 1950s as part of his work 
 on associating affine group schemes with groups over integers. For infinit
 e-dimensional Kac-Moody groups\, it remains an open problem. To state this
  problem more precisely\, let $\\mathfrak g$ be a symmetrizable Kac–Mood
 y algebra over $\\mathbb Q$\, $V$ be an integrable highest weight $\\mathf
 rak g$-module\, and $V_{\\mathbb Z}$ be a $\\mathbb Z$-form of $V$. Let $G
 =G(\\mathbb{Q})$ be an associated minimal representation-theoretic Kac–M
 oody group and let $G(\\mathbb{Z})$ be its integral subgroup. Suppose $\\G
 amma(\\mathbb{Z})$ is the Chevalley subgroup of $G$\, that is\, the subgro
 up that stabilizes the lattice $V_{\\mathbb Z}$ in $V$. The integrality fo
 r $G$ is to determine if $G(\\mathbb{Z})=\\Gamma(\\mathbb{Z})$. We will di
 scuss some progress on this problem\, which we made in a joint work with L
 isa Carbone\, Dongwen Liu\, and Scott H. Murray. Our results have various 
 applications\, including the integrality of subgroups of the unipotent sub
 group $U$ of $G$ that are generated by commuting real root groups.\n\nHybr
 id delivery (in person on University of Saskatchewan campus and via Zoom).
 \n
LOCATION:https://researchseminars.org/talk/PIMS_GAP/15/
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