Polynomial Realization of the Uq(sl(3)) Gel’Fand-(Weyl)-Zetlin Basis and Irregular Irreps at Roots of Unity

V. K. Dobrev and P. Truini
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V. K. Dobrev: Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences
P. Truini: dell’Universitá di Genova, Nazionale di Fisica Nucleare, Sezione di Genova, Dipartimento di Fisica

A chapter in Symmetries in Science X, 1998, pp 79-119 from Springer

Abstract: Abstract This contribution is dedicated to L. C. Biedenharn. It represents a natural development of our joint paper with Larry [1] in which we gave the construction of arbitrary lowest weight (holomorphic) representations of U q (sl(n)) in terms of polynomials ofn(n− l)/2 (real or complex) variables, most explicitly for n= 3, on which the generators of U q (sl(n)) act as q-difference operators. As we know such explicit realizations are very important for the applications in physics. Here we extend the results of [1] to give a polynomial realization of the so-called Gel’fand-(Weyl)-Zetlin (GWZ) basis, which is also very important for the physics applications. We first recall the notions.

Keywords: Lower Weight; Quantum Group; Singular Vector; Verma Module; Polynomial Solution (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1007/978-1-4899-1537-5_5

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