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SUMMARY:Li Yu (University of Chicago)
DTSTART:20201203T195000Z
DTEND:20201203T205000Z
DTSTAMP:20260423T005749Z
UID:GPRTatNU/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GPRTatNU/13/
 ">Wonderful compactification of a Cartan subalgebra of a semisimple Lie al
 gebra</a>\nby Li Yu (University of Chicago) as part of Geometry\, Physics\
 , and Representation Theory Seminar\n\n\nAbstract\nLet $H$ be a Cartan sub
 group of a semisimple algebraic group $G$ over the complex numbers. The wo
 nderful compactification $\\overline{H}$ of $H$ was introduced and studied
  by De Concini and Procesi. For the Lie algebra $\\mathfrak{h}$ of $H$\, w
 e define an analogous compactification $\\overline{\\mathfrak{h}}$ of $\\m
 athfrak{h}$\, to be referred to as the wonderful compactification of $\\ma
 thfrak{h}$. The wonderful compactification of $\\mathfrak{h}$ is an exampl
 e of an "additive toric variety". We establish a bijection between the set
  of irreducible components of the boundary $\\overline{\\mathfrak{h}} - \\
 mathfrak{h}$ of $\\mathfrak{h}$ and the set of maximal closed root subsyst
 ems of the root system for $(G\, H)$ of rank $r - 1\,$ where $r$ is the di
 mension of $\\mathfrak{h}$. An algorithm based on Borel-de Siebenthal theo
 ry that constructs all such root subsystems is given. We prove that each i
 rreducible component of $\\overline{\\mathfrak{h}}- \\mathfrak{h}$ is isom
 orphic to the wonderful compactification of a Lie subalgebra of $\\mathfra
 k{h}$ and is of dimension $r - 1$.  In particular\, the boundary $\\overli
 ne{\\mathfrak{h}} - \\mathfrak{h}$ is equidimensional. We describe a large
  subset of the regular locus of $\\overline{\\mathfrak{h}}$. As a conseque
 nce\, we prove that $\\overline{\\mathfrak{h}}$ is a normal variety.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/13/
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