Gelfand-Tsetlin modules over $\mathfrak{gl}(n,\mathbb{C})$ with arbitrary characters

Abstract

A Gelfand-Tsetlin tableau $T(v)$ induces a character ${\chi }_v$ of the Gelfand-Tsetlin subalgebra $\Gamma$ of $U=U(\mathfrak{gl}(n,\mathbb{C}))$. By a theorem due to Ovsienko, for each tableau $T(v)$ there exists a finite number of nonisomorphic irreducible Gelfand-Tsetlin modules with ${\chi }_v$ in its support, though explicit examples of such modules are only known for special families of characters. In this article we build a family of Gelfand-Tsetlin modules parametrized by characters, such that each character appears in its corresponding module. We also find the support of these modules, with multiplicities.

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References in corpus (1)

• Irreducible Generic Gelfand-Tsetlin Modules of $\mathfrak{gl}(n)$

Cited by in corpus (2)

• Principal Galois orders and Gelfand-Zeitlin modules
• Gelfand-Tsetlin modules of quantum gl_n$defined by admissible sets of relations