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UID:d02330f9ea8b9d3248799621e6677c22
CATEGORIES:Lie Group Quantum Mathematics Seminar
CREATED:20230206T104632
SUMMARY:Quantum Weyl algebras and a new First Fundamental Theorem of invariant theory for U_q(gl(n))
LOCATION:Zoom
DESCRIPTION:<p><strong>Abstract </strong>The First Fundamental Theorem (FFT) is one of 
 the highlights of invariant theory of reductive groups and goes back to the
  works of Schur, Weyl, Brauer, etc. For the group GL(V), the FFT describes 
 generators for polynomial invariants on direct sums of several copies of th
 e standard module V and 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 algebra of polynomial-coefficient differential operators).</p><
 p>In this talk we first construct a quantum Weyl algebra and then present a
  quantum analogue of the FFT. We explain the relation between the FFT and a
  double centralizer property inside the quantum Weyl algebra. We remark tha
 t the FFT that we obtain 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 c
 onnection between this work and the Capelli Eigenvalue Problem in the conte
 xt of quantum symmetric spaces. This talk is based on a joint project with 
 Gail Letzter and Siddhartha Sahi.</p>
CONTACT:Hadi Salmasian, University of Ottawa
X-EXTRAINFO:Zoom link https://rutgers.zoom.us/j/93921465287\nMeeting ID: 939 2146 5287\
 nPasscode: 196884, the dimension of the weight 2 homogeneous\nsubspace of t
 he moonshine module
DTSTAMP:20260907T040917
DTSTART;TZID=America/New_York:20230210T121000
DTEND;TZID=America/New_York:20230210T131000
SEQUENCE:0
TRANSP:OPAQUE
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