Fibers of characters in Gelfand-Tsetlin categories

By Vyacheslav Futorny, S. Ovsienko. 2014

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. For a class of noncommutative rings, called Galois orders, we study the problem of an extension of characters from a commutative subalgebra. We show that for Galois orders this problem is always solvable in the sense that all characters can be extended, moreover, in finitely many ways, up to isomorphism. These results can be viewed as a noncommutative analogue of liftings of prime ideals in the case of integral extensions of commutative rings. The proposed approach can be applied to the representation theory of many infinite dimensional algebras including universal enveloping algebras of reductive Lie algebras (in particular gl n ), Yangians and finite W -algebras. As an example we recover the theory of Gelfand-Tsetlin modules for gl n .

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2f307ce315772a05c9cf9ca11aab99127b4dda9f