Geometric construction of Gelfand-Tsetlin modules over simple Lie algebras

摘要

In the present paper we describe a new class of Gelfand-Tsetlin modules for an arbitrary complex simple finite-dimensional Lie algebra g and give their geometric realization as the space of 'delta-functions' on the flag manifold G/B supported at the 1-dimensional submanifold. When g = sl(n, C) (or gl(n, C)) these modules form a subclass of Gelfand-Tsetlin modules with infinite-dimensional weight subspaces. We discuss their properties and describe the simplicity criterion for these modules in the case of the Lie algebra sl(3, C). (C) 2019 Elsevier B.V. All rights reserved.