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DTSTART;TZID=America/Toronto:20250620T114500
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URL:https://uwaterloo.ca/pure-mathematics/events/phd-defence
SUMMARY:PhD Defence
CLASS:PUBLIC
DESCRIPTION:NICOLE KITT\, UNIVERSITY OF WATERLOO\n\n_Characterizing Cofree 
 Representations of SL_n x SL_m_\n\nThe study\, and in particular classific
 ation\, of cofree representations\nhas been an interest of research for ov
 er 70 years. The\nChevalley-Shepard Todd Theorem provides a beautiful intr
 insic\ncharacterization for cofree representations of finite groups.\nSpec
 ifically\, this theorem says that a representation V of a finite\ngroup G 
 is cofree if and only if G is generated by pseudoreflections.\nUp until th
 e late 1900s\, with the exception of finite groups\, all of\nthe existing 
 classifications of cofree representations of a particular\ngroup consist o
 f an explicit list\, as opposed to an intrinsic\ngroup-theoretic character
 ization. However\, in 2019\, Edidin\, Satriano\,\nand Whitehead formulated
  a conjecture which intrinsically\ncharacterizes stable irreducible cofree
  representations of connected\nreductive groups and verified their conject
 ure for simple Lie groups.\nThe conjecture states that for a stable irredu
 cible representation V\nof a connected reductive group G\, V is cofree if 
 and only if V is\npure. In comparison to the classifications comprised of 
 a list of\ncofree representations\, this conjecture can be viewed as an an
 alogue\nof the Chevalley–Shepard–Todd Theorem for actions of connected
 \nreductive groups. The aim of this thesis is to further expand upon the\n
 techniques formulated by Edidin\, Satriano\, and Whitehead as a means to\n
 work towards the verification of the conjecture for all connected\nsemisim
 ple Lie groups. The main result of this thesis is the\nverification of the
  conjecture for stable irreducible representations\nV\\otimes W of SL_n x 
 SL_m satisfying dim V>=n^2 and dim W>=m^2.
DTSTAMP:20260504T123150Z
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