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Theoretical and Mathematical Physics

, Volume 198, Issue 1, pp 145–155 | Cite as

Construction of the Gelfand–Tsetlin Basis for Unitary Principal Series Representations of the Algebra sln(ℂ)

  • P. A. ValinevichEmail author
Article
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Abstract

We consider infinite-dimensional unitary principal series representations of the algebra sln(), implemented on the space of functions of n(n−1)/2 complex variables. For such representations, the elements of the Gelfand–Tsetlin basis are defined as the eigenfunctions of a certain system of quantum minors. The parameters of these functions, in contrast to the finite-dimensional case, take a continuous series of values. We obtain explicit formulas that allow constructing these functions recursively in the rank of the algebra n. The main construction elements are operators intertwining equivalent representations and also a group operator of a special type. We demonstrate how the recurrence relations work in the case of small ranks.

Keywords

Gelfand–Tsetlin basis intertwining operator unitary principal series representation 

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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of SciencesSt. PetersburgRussia

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