Gelfand-Zetlin basis for \(U_ q(\mathfrak{gl}(\text{\textbf{N}}+\text{\textbf{1}}))\) modules.

DOI10.1007/BF00399970zbMath0685.17004OpenAlexW2329103142MaRDI QIDQ1825939

Kimio Ueno, Tadayoshi Takebayashi, Youichi Shibukawa

Publication date: 1989

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00399970

zbMATH Keywords

irreducible modulesbranching ruleslowering operatorsGelfand-Zetlin basisquantum universal enveloping algebra

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Universal enveloping (super)algebras (17B35)

Related Items (20)

Yangians and Gelfand-Zetlin bases ⋮ Solution of a \(q\)-difference Noether problem and the quantum Gelfand-Kirillov conjecture for \(\mathfrak{gl}_N\) ⋮ Construction of Gelfand-Tsetlin basis for \({\mathcal U}_ q(gl(N+1))\)- modules ⋮ Contractions of the irreducible representations of the quantum algebras suq(2) and soq(3) ⋮ Matrix elements and Wigner coefficients for U q[gl(n)] ⋮ Reduced Wigner coefficients for U q[gl(n)] ⋮ Symmetries of Clebsch–Gordan coefficients of the quantum group U q(n) ⋮ Gelfand-Tsetlin modules of quantum \(\mathfrak{gl}_n\) defined by admissible sets of relations ⋮ Irregular Uq (sl(3)) representations at roots of unity via Gel’fand–(Weyl)–Zetlin basis ⋮ Polynomial realization of the Uq(sl(3)) Gel’fand–(Weyl)–Zetlin basis ⋮ Periodic and partially periodic representations of \(\text{SU}(N)_ q\) ⋮ Normalized Uq(sl(3)) Gel’fand–(Weyl)–Zetlin basis and new summation formulas for q-hypergeometric functions ⋮ Step algebras of quantum \({\mathfrak{sl}}(n)\) ⋮ Irreducible subquotients of generic Gelfand-Tsetlin modules over \(U_q(\mathfrak{gl}_n)\) ⋮ Explicit construction of irreducible modules for \(U_q(\mathfrak{gl}_n)\) ⋮ Gelfand–Tsetlin Bases for Classical Lie Algebras ⋮ Schur-Weyl reciprocity for Ariki-Koike algebras ⋮ Raising and lowering operators for U q (gl(n)) ⋮ Quantized Vershik-Kerov theory and quantized central measures on branching graphs ⋮ The induction coefficients of the Hecke algebra and the Clebsch–Gordan coefficients of the quantum group SUq(N). II. General Gel’fand basis

Cites Work

• Unnamed Item
• A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
• Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra

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