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SUMMARY:Discrete evolution operator for $q$-deformed isotropic top - Isaev
 \, A (BLTP JINR)
DTSTART:20090325T100000Z
DTEND:20090325T110000Z
UID:TALK17539@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The structure of a cotangent bundle is investigated for quantu
 m linear groups $GL_q(n)$ and $SL_q(n)$. Using a $q$-version of the Cayley
 -Hamilton theorem we construct an extension of the algebra of differential
  operators on $SL_q(n)$ by spectral values of the matrix of right invarian
 t vector fields. We consider two applications for the spectral extension. 
 First\, we describe the extended Heisenberg double in terms of a new set o
 f generators --- the Weyl partners of the spectral variables. Calculating 
 defining relations in terms of these generators allows us to derive $SL_q(
 n)$ type dynamical R-matrices in a surprisingly simple way. Second\, we ca
 lculate discrete evolution operator for the model of $q$-deformed isotropi
 c top introduced by A.Alekseev and L.Faddeev. The evolution operator is no
 t uniquely defined and we present two possible expressions for it. The fir
 st one is a Riemann theta function in the spectral variables. The second o
 ne is an almost free motion evolution operator in terms of logarithms of t
 he spectral variables. Relation between the two operators is given by a mo
 dular functional equation for Riemann theta function.
LOCATION:Seminar Room 1 Newton Institute
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