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SUMMARY:Kenny De Commer (Vrije Universiteit Brussel\, Belgium)
DTSTART:20201123T150000Z
DTEND:20201123T160000Z
DTSTAMP:20260404T163232Z
UID:QGS/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/QGS/3
 /">A quantization of Sylvester's law of inertia</a>\nby Kenny De Commer (V
 rije Universiteit Brussel\, Belgium) as part of Quantum Groups Seminar [QG
 S]\n\n\nAbstract\nSylvester's law of inertia states that two self-adjoint 
 matrices A and B are related as $A = X^*BX$ for some invertible complex ma
 trix $X$ if and only if $A$ and $B$ have the same signature $(N_+\,N_-\,N_
 0)$\, i.e. the same number of positive\, negative and zero eigenvalues. In
  this talk\, we will discuss a quantized version of this law: we consider 
 the reflection equation *-algebra (REA)\, which is a quantization of the *
 -algebra of polynomial functions on self-adjoint matrices\, together with 
 a natural adjoint action by quantum $GL(N\,\\mathbb{C})$. We then show tha
 t to each irreducible bounded *-representation of the REA can be associate
 d an extended signature $(N_+\,N_-\,N_0\,[r])$ with $[r]$ in $\\mathbb{R}/
 \\mathbb{Z}$\, and we will explain in what way this is a complete invarian
 t of the orbits under the action by quantum $GL(N\,\\mathbb{C})$. This is 
 part of a work in progress jointly with Stephen Moore.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/3/
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