A classification of lowest weight irreducible modules over Z22-graded extension of <i>osp</i>(1|2)
K. Amakawa, N. Aizawa
Abstract
We investigate representations of the Z22-graded extension of osp(1|2), which is the spectrum generating algebra of the recently introduced Z22-graded version of superconformal mechanics. The main result is a classification of irreducible lowest weight modules of the Z22-graded extension of osp(1|2). This is done via the introduction of Verma modules and its maximal invariant submodule generated by singular vectors. Explicit formulas of all singular vectors are also presented.
Topics & Concepts
Verma moduleMathematicsExtension (predicate logic)Invariant (physics)Pure mathematicsAlgebra over a fieldSpectrum (functional analysis)Irreducible representationWeightInvariant theoryDiscrete mathematics(g,K)-moduleCombinatoricsAlgebraic structures and combinatorial modelsHomotopy and Cohomology in Algebraic TopologyAdvanced Topics in Algebra