Infinite-dimensional representations of the Lie algebra \(\mathfrak{gl}(n,\mathbb C)\) related to complex analogs of the Gelfand-Tsetlin patterns and general hypergeometric functions on the Lie group \(\text{GL}(n,\mathbb C)\).

Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

Related Items (16)

Weight representations of admissible affine vertex algebras ⋮ The Gelfand–Tsetlin basis for infinite-dimensional representations of gln(C) ⋮ Fibers of characters in Gelfand-Tsetlin categories ⋮ New singular Gelfand-Tsetlin \(\mathfrak{gl}(n)\)-modules of index 2 ⋮ De Concini-Kac filtration and Gelfand-Tsetlin generators for quantum \(\mathfrak{gl}_N\) ⋮ Gelfand-Tsetlin modules of quantum \(\mathfrak{gl}_n\) defined by admissible sets of relations ⋮ Singular Gelfand-Tsetlin modules of \(\mathfrak{gl}(n)\) ⋮ Combinatorial construction of Gelfand-Tsetlin modules for \(\mathfrak{gl}_n\) ⋮ Torsion theories induced from commutative subalgebras. ⋮ A continuous analogue of Gelfand-Tsetlin schemes and a realization of the principal series of irreducible unitary representations of the group \(\mathrm{GL}(n, \mathbb{C})\) in the space of functions on the variety of these schemes ⋮ Irreducible subquotients of generic Gelfand-Tsetlin modules over \(U_q(\mathfrak{gl}_n)\) ⋮ Explicit construction of irreducible modules for \(U_q(\mathfrak{gl}_n)\) ⋮ Geometric construction of Gelfand-Tsetlin modules over simple Lie algebras ⋮ Construction of the Gelfand-Tsetlin basis for unitary principal series representations of the algebra \(sl_n(\mathbb{C})\) ⋮ Gelfand-Tsetlin modules of 𝔰𝔩(3) in the principal block ⋮ Classification of simple Gelfand–Tsetlin modules of 𝔰𝔩(3)

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