Racah problems for the oscillator algebra, the lie algebra sln, and multivariate Krawtchouk polynomials

The oscillator Racah algebra R-n(h) is realized by the intermediate Casimir operators arising in the multifold tensor product of the oscillator algebra h. An embedding of the Lie algebra sl(n-1) into R-n(h) is presented. It relates the representation theory of the two algebras. We establish the connection between recoupling coefficients for h and matrix elements of sl(n)-representations which are both expressed in terms of multivariate Krawtchouk polynomials of Griffiths type