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UID:19f3ffd75e7ef5b7a8600e39476a24e0
CATEGORIES:Algebra Seminar
CREATED:20241127T172349
SUMMARY:Modular Reduction of Nilpotent Orbits
LOCATION:H705
DESCRIPTION:<pre><span style="font-size: large;" size="4"><strong>Modular Reduction of 
 Nilpotent Orbits(Jay Taylor, Dec. 4, 2024)</strong><br>The general linear g
 roup G=GL<sub>n</sub>(k) over a field k acts on the space <frak>gl=<frak>gl
 <sub>n</sub> of (nxn)-matrices by conjugation. The set N(g) of nilpotent ma
 trices is preserved by this action and G acts with finitely many orbits. Th
 e Jordan normal form gives a representative of each orbit that is contained
  in <frak>gl<sub>n</sub>(Z). Importantly, the structure of the centralizer 
 of this nilpotent matrix is independent of k.<br>It is natural to ask to wh
 at extent this statement extends to aconnected reductive algebraic group G 
 acting on its Lie algebra <frak>g or the dual space <frak>g* via the (co-)a
 djoint representation. In general, thestructure of centralisers of nilpoten
 t elements will depend on k butone can hope that the centraliser dimension 
 remains the same. In thistalk I will propose two variants of this idea, gen
 eralising theclassical situation above, and report on on-going joint work w
 ith AdamThomas (Warwick) to establish the existence of elements satisfying 
 theproposed properties.</frak></frak></frak></frak></frak></span></pre>
CONTACT:Jay Taylor
DTSTAMP:20260828T093431
DTSTART;TZID=America/New_York:20241127T080000
DTEND;TZID=America/New_York:20241127T170000
SEQUENCE:0
TRANSP:OPAQUE
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