Seminar
Racah problems for the oscillator algebra and sl(n)
by Wouter Van de Vijver (Ghent University)
Location: Campus Sterre, Building S8, Classroom 3.2, Ghent
Time: Friday May 17, 2019 at
14:30
We consider the tensor product of \(n\) copies of the oscillator algebra \(h\). Using the Hopf structure and Casimir operator of \(h\), we construct a subalgebra \(R_n(h)\) in the same way the higher rank Racah algebra was constructed for \(su(1; 1)\) in [1]. One can embed the algebra \(R_n(h)\) into \(sl(n,1)\) after an affine transformation of the generators by central elements. We study the connection between recoupling coefficients for hand \(sl(n)\)-representations. These coefficients turn out to be multivariate Krawtchouck polynomials. The relation with the Wigner-\((3nj)\) symbols for h is explained. Flipping two factors in the tensor product is a symmetry of \(Rn(h)\). This leads to an automorphism of \(sl(n,1)\). The corresponding group elements of \(SL(n,1)\) are constructed.
