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SUMMARY:Amy Huang (Texas A&M University)
DTSTART:20240730T083000Z
DTEND:20240730T093000Z
DTSTAMP:20260422T155902Z
UID:HKUST-AG/53
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HKUST-AG/53/
 ">Syzygies of determinantal thickenings and gl(m|n) representations</a>\nb
 y Amy Huang (Texas A&M University) as part of Algebra and Geometry Seminar
  @ HKUST\n\nLecture held in Room 2463 (Lift 25/26).\n\nAbstract\nThe coord
 inate ring $S = \\mathbb{C}[x_{i\,j}]$ of space of $m \\times n$ matrices 
 carries an action of the group $\\mathrm{GL}_m \\times \\mathrm{GL}_n$ via
  row and column operations on the matrix entries. If we consider any $\\ma
 thrm{GL}_m \\times \\mathrm{GL}_n$-invariant ideal $I$ in $S$\, the syzygy
  modules $\\mathrm{Tor}_i(I\,\\mathbb{C})$ will carry a natural action of 
 $\\mathrm{GL}_m \\times \\mathrm{GL}_n$. Via BGG correspondence\, they als
 o carry an action of $\\bigwedge^{\\bullet} (\\mathbb{C}^m \\otimes \\math
 bb{C}^n)$. It is a result by Raicu and Weyman that we can combine these ac
 tions together and make them modules over the general linear Lie superalge
 bra $\\mathfrak{gl}(m|n)$. We will explain how this works and how it enabl
 es us to compute all Betti numbers of any $\\mathrm{GL}_m \\times \\mathrm
 {GL}_n$-invariant ideal $I$.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/53/
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