Polynomial realization of the Uq(sl(3)) Gel’fand–(Weyl)–Zetlin basis
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Publication:4352192
DOI10.1063/1.532074zbMath0882.17005OpenAlexW2072616219MaRDI QIDQ4352192
Piero Truini, Vladimir K. Dobrev
Publication date: 2 March 1998
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.532074
quantum groupspolynomial functions\(q\)-difference operatorsShapovalov formlowest weight representationsGel'fand-Zetlin basisGWZ basis
Related Items (6)
A functional realization of the Gelfand-Tsetlin base ⋮ Factorization of the \(R\)-matrix for the quantum algebra \({U_q(s\ell_n)}\) ⋮ Normalized Uq(sl(3)) Gel’fand–(Weyl)–Zetlin basis and new summation formulas for q-hypergeometric functions ⋮ Gelfand–Tsetlin Bases for Classical Lie Algebras ⋮ A Gelfand-Tsetlin-type basis for the algebra \(\mathfrak{sp}_4\) and hypergeometric functions ⋮ Construction of the Gelfand-Tsetlin basis for unitary principal series representations of the algebra \(sl_n(\mathbb{C})\)
Cites Work
- Canonical construction of differential operators intertwining representations of real semisimple Lie groups
- A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
- Periodic and partially periodic representations of \(\text{SU}(N)_ q\)
- An extension of the Borel-Weil construction to the quantum group \(U_ q(n)\)
- Gelfand-Zetlin basis for \(U_ q(\mathfrak{gl}(\text{\textbf{N}}+\text{\textbf{1}}))\) modules.
- On a bilinear form on the universal enveloping algebra of a complex semisimple Lie algebra
- q-analogs of IU(n) and U(n,1)
- Complementarity of suq(3) and uq(2) and q-boson realization of the suq(3) irreducible representations
- Representation theory approach to the polynomial solutions of q-difference equations: Uq(sl(3)) and beyond
- Irregular Uq (sl(3)) representations at roots of unity via Gel’fand–(Weyl)–Zetlin basis
- Raising and lowering operators for uq(n)
- On the Representations of the Semisimple Lie Groups. II
- Class of Representations of the IU(n) and IO(n) Algebras and Respective Deformations to U(n, 1), O(n, 1)
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