Deformed Clifford Cl_q(n|m) and orthosymplectic U_q[osp(2n+1|2m)] superalgebras and their root of unity representations

Details Deformed Clifford Cl_q(n|m) and orthosymplectic U_q[osp(2n+1|2m)] superalgebras and their root of unity representations Deformed Clifford Cl_q(n|m) and orthosymplectic U_q[osp(2n+1|2m)] superalgebras and their root of unity representations

2002-10-22

arxiv.org/abs/math/0210340v1

J.Phys.A35:9367-9380,2002

Mathematics

Quantum Algebra

15 pages

Scientific paper

10.1088/0305-4470/35/44/307

It is shown that the Clifford superalgebra Cl(n|m) generated by m pairs of Bose operators (odd elements) anticommuting with n pairs of Fermi operators (even elements) can be deformed to Cl_q(n|m) such that the latter is a homomorphic image of the quantum superalgebra U_q[osp(2n+1|2m)]. The Fock space F(n|m) of Cl_q(n|m) is constructed. At q being a root of unity (q=\exp ({i\pi l/k})) q-bosons (and q-fermions) are operators acting in a finite-dimensional subspace F_{l/k}(n|m) of F(n|m). Each F_{l/k}(n|m) is turned through the above mentioned homomorphism into an irreducible (root of unity) U_q[osp(2n+1|2m)] module. For q being a primitive root of unity (l=1) the corresponding representation is unitary. The module F_{1/k}(n|m) is decomposed into a direct sum of irreducible U_q[sl(m|n)] submodules. The matrix elements of all Cartan-Weyl elements of U_q[sl(m|n)] are given within each such submodule.

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