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DTSTAMP:20250809T002343Z
DESCRIPTION:Title: Quantum groups\, quantum Weyl algebras\, and a new First
  Fundamental Theorem of invariant theory for $U_q(gl(n))$\n\nAbstract:The 
 First Fundamental Theorem (FFT) is one of the highlights of invariant theo
 ry of reductive groups and goes back to the works of Schur\, Weyl\, Brauer
 \, etc. For the group $GL(V)$\, the FFT describes generators for polynomia
 l invariants on direct sums of several copies of the standard module $V$ a
 nd its dual $V*$. Then R. Howe pointed out that the FFT is closely related
  to a double centralizer statement inside a Weyl algebra (a.k.a. the algeb
 ra of polynomial-coefficient differential operators).\n	\n	In this talk we f
 irst construct a quantum Weyl algebra and then present a quantum analogue 
 of the FFT. As a special case of this FFT we obtain a double centralizer s
 tatement inside our quantum Weyl algebra. We remark that the FFT that we o
 btain is different from the one proved by G. Lehrer\, H. Zhang\, and R.B. 
 Zhang for U_q(gl(n)). Time permitting\, I will explain the connection betw
 een this work and the Capelli Eigenvalue Problem for classical quantum gro
 ups. This talk is based on a joint project with Gail Letzter and Siddharth
 a Sahi.\n\nSalle PK-5115\, Pavillon Président-Kennedy\, 201 rue Président-
 Kennedy\, Montreal\n\nWeb site : https://lacim.uqam.ca/seminaires/\n
DTSTART:20230203T160000Z
DTEND:20230203T170000Z
SUMMARY:Hadi Salamsian (University of Ottawa)
URL:/mathstat/channels/event/hadi-salamsian-university
 -ottawa-345741
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