Centre and Representations of U_q(sl(2|1)) at Roots of Unity

Abstract

Quantum groups at roots of unity have the property that their centre is enlarged. Polynomial equations relate the standard deformed Casimir operators and the new central elements. These relations are important from a physical point of view since they correspond to relations among quantum expectation values of observables that have to be satisfied on all physical states. In this paper, we establish these relations in the case of the quantum Lie superalgebra U_q(sl(2|1)). In the course of the argument, we find and use a set of representations such that any relation satisfied on all the representations of the set is true in U_q(sl(2|1)). This set is a subset of the set of all the finite dimensional irreducible representations of U_q(sl(2|1)), that we classify and describe explicitly.

Minor corrections, References added. LaTeX2e, 18 pages, also available at http://lapphp0.in2p3.fr/preplapp/psth/ENSLAPP583.ps.gz . To appear in J. Phys. A: Math. Gen

References in corpus (4)

• Finite-dimensional representations of the quantum superalgebra $U_q[gl(n/m)]$ and related q-identities
• Classical and Quantum sl(1|2) Superalgebras, Casimir Operators and Quantum Chain Hamiltonians
• Unitarizable Representations of the Deformed Para-Bose Superalgebra Uq[osp(1/2)] at Roots of 1
• Finite Dimensional Representations of the Quantum Superalgebra $U_q[gl(3/2)]$ in a Reduced $U_q[gl(3/2)]\supset U_q[gl(3/1)]\supset U_q[gl(3)]$ Basis

Cited by in corpus (5)

• Toward logarithmic extensions of ^sl(2)_k conformal field models
• Quasi-lisse extension of affine ${\mathfrak{sl}}_2$ à la Feigin--Tipunin
• Quantum superalgebras at roots of unity and non-abelian symmetries of integrable models
• Quantum Supergroup $U_{r,s}(osp(1,2))$, Scasimir Operators, and Dickson polynomials
• Graded q-pseudo-differential Operators and Supersymmetric Algebras