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SUMMARY:Nilpotent commuting varieties and support varieties
DTSTART:20151013T151500
DTEND:20151013T170000
DTSTAMP:20260415T024341Z
UID:cc4519a089c1f76cf3dee8b8e6e7d61f631cc1caba4a3d4aaf8bf606
CATEGORIES:Conferences - Seminars
DESCRIPTION:Paul Levy (Lancaster)\nAbstract :\nCommuting varieties are cla
 ssical objects of study in Lie theory. Historically the first result was t
 he proof by Motzkin-Taussky in 1955 (established independently by Gerstenh
 aber) that the variety of pairs of commuting n x n matrices is irreducible
 . Richardson extended this to an arbitrary reductive Lie algebra in charac
 teristic zero. More recently there has been interest in the subvariety of 
 pairs of commuting nilpotent elements. One highlight was Premet's proof th
 at this nilpotent commuting variety of a reductive Lie algebra is equidime
 nsional\, and is irreducible for \\gl_n.\n\nHere I will explore two variat
 ions on this theme. First of all\, I will introduce some generalisations o
 f the nilpotent commuting variety\, for which we confine the first coordin
 ate to a fixed nilpotent orbit closure. The main task here is to determine
  the irreducible components and their dimension. This is joint work with N
 . Ngo. Secondly\, I will summarize some recent results on the variety of r
 -tuples of commuting nilpotent elements of \\gl_n or \\sp_{2n}. This is jo
 int work with N. Ngo and K. Sivic.\n\nThe main applications of this work a
 re to cohomology and representation theory of Frobenius kernels of simple 
 algebraic groups (the support varieties of the title). These applications 
 are somewhat more esoteric than the main subject matter\, so I will reserv
 e most of the details for the second part of the talk.
LOCATION:CHB331 http://plan.epfl.ch/?lang=fr&room=CHB331
STATUS:CONFIRMED
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