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

DOI10.1134/S1064562407010103zbMath1327.22017MaRDI QIDQ492434

Mark I. Graev

Publication date: 20 August 2015

Published in: Doklady Mathematics (Search for Journal in Brave)

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Representation theory for linear algebraic groups (20G05) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

Related Items (7)

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 ⋮ Restriction of representations of \(\mathrm{GL}(n + 1, \mathbb{C})\) to \(\mathrm{GL}(n, \mathbb{C})\) and action of the Lie overalgebra ⋮ 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)

Cites Work

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• 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 \(\text{GL}(n,\mathbb C)\).

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