Abstract:In this paper, we study an analogue of the Bernstein–Gelfand–Gelfand category
${\mathcal {O}}$
for truncated current Lie algebras
$\mathfrak {g}_n$
attached to a complex semisimple Lie algebra. This category admits Verma modules and simple modules, each parametrized by the dual space of the truncated currents on a choice of Cartan subalgebra in
$\mathfrak {g}$
. Our main result describes an inductive procedure for computin… Show more
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