A geometric approach to 1-singular Gelfand-Tsetlin gln-modules

This paper is devoted to an elementary new construction of 1-singular Gelfand-Tsetlin modules using complex geometry. We introduce a universal ring Dv together with the vector space S=S(Dv) with basis Bv=B(Dv) consisted of some local distributions such that S is a natural Dv-module. For any homomorphism of rings U(h)→Dv, where h is a Lie algebra, it follows that S is also an h-module. We observe that the homomorphism of rings constructed in [8] is a homomorphism of type U(gln(C))→Dv. Using this observation we obtain a construction of the universal 1-singular Gelfand-Tsetlin gln(C)-module from [7].