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SUMMARY:Kenny De Commer (Vrije Universiteit Brussel\, Belgium)
DTSTART:20201123T150000Z
DTEND:20201123T160000Z
DTSTAMP:20260422T175216Z
UID:QGS/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/QGS/3/">A qu
 antization of Sylvester's law of inertia</a>\nby Kenny De Commer (Vrije Un
 iversiteit Brussel\, Belgium) as part of Quantum Groups Seminar [QGS]\n\n\
 nAbstract\nSylvester's law of inertia states that two self-adjoint matrice
 s A and B are related as $A = X^*BX$ for some invertible complex matrix $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 t
 alk\, we will discuss a quantized version of this law: we consider the ref
 lection equation *-algebra (REA)\, which is a quantization of the *-algebr
 a of polynomial functions on self-adjoint matrices\, together with a natur
 al adjoint action by quantum $GL(N\,\\mathbb{C})$. We then show that to ea
 ch irreducible bounded *-representation of the REA can be associated an ex
 tended signature $(N_+\,N_-\,N_0\,[r])$ with $[r]$ in $\\mathbb{R}/\\mathb
 b{Z}$\, and we will explain in what way this is a complete invariant of th
 e 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://researchseminars.org/talk/QGS/3/
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