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SUMMARY:Jeffrey Adams (University of Maryland)
DTSTART:20220818T143000Z
DTEND:20220818T160000Z
DTSTAMP:20260422T150051Z
UID:atlas/33
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/atlas/33/">H
 ermitian forms on finite- dimensional representations</a>\nby Jeffrey Adam
 s (University of Maryland) as part of Real reductive groups/atlas\n\n\nAbs
 tract\nThe study of signatures of Hermitian forms on finite dimensional re
 presentations serves as an example of the general theory\, while having so
 me special features\, and being surprisingly interesting in its own right.
 \n\nThe finite dimensional representations of the real forms $G(\\mathbb R
 )$ of $G(\\mathbb C$) are essentially independent of the real form. Howeve
 r these representations are all unitary if and only if $G(\\mathbb R)$ is 
 compact\, and the signature of the Hermitian forms depend very much on the
  real form. \n\nWe'll talk about computing this\, using an elementary form
 ula (arising from the Atlas theory of the c-form)in terms of the Weyl char
 acter formula. We'll also discuss some interesting invariants for a finite
  dimensional representation: the Frobenius/Schur indicator and the real-qu
 aternionic indicator.\n
LOCATION:https://researchseminars.org/talk/atlas/33/
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