qanalogue of IU (n) for q a root of unity
Abstract
Periodic and partially periodic representations of U(IU(n))_{q} are constructed for q^{m} = 1, m being an odd or even integer. The classical nonsemisimple IU (n) or U (n)⋉I_{2n} algebra has an abelian subalgebra of dimension 2n. GelfandZetlin bases and matrix elements are generalized and adapted to this case. Our previous results for U(IU(n))_{q} for a generic q (not a root of unity) and those for SU(N)_{q} for q^{m} = 1 are combined in the present study giving explicit matrix elements and eigenvalues such as the second order Casimilar operator D_{2} = K^{2} cos(2π/m)(h_{2n+1}+ ... + h_{nn+1} + n  1)/cos(2π/m). This displays the role of the internal parameters (h_{i,n+1}) in the qanalogue of the classical K^{2} (``mass'' squared). The two translation generators (I_{n}^{n+1}, I_{n+1}^{n}) become periodic.
 Publication:

Physics Letters B
 Pub Date:
 February 1991
 DOI:
 10.1016/03702693(91)90242I
 Bibcode:
 1991PhLB..255..242A