Construction of Gelfand-Tsetlin basis for \({\mathcal U}_ q(gl(N+1))\)- modules

DOI10.2977/prims/1195170852zbMath0718.17013OpenAlexW2241301269MaRDI QIDQ2639153

Tadayoshi Takebayashi, Youichi Shibukawa, Kimio Ueno

Publication date: 1990

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195170852

zbMATH Keywords

quantum groupGelfand-Tsetlin basis

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37)

Related Items

Zonal spherical functions on quantum symmetric spaces and MacDonald's symmetric polynomials, Generic Gelfand-Tsetlin representations of Uqtw(𝔰𝔬3) and Uqtw(𝔰𝔬4), Generic Gelfand-Tsetlin modules of quantized and classical orthogonal algebras, Gelfand-Tsetlin modules of quantum \(\mathfrak{gl}_n\) defined by admissible sets of relations, Theq-difference Noether problem for complex reflection groups and quantum OGZ algebras, Irreducible subquotients of generic Gelfand-Tsetlin modules over \(U_q(\mathfrak{gl}_n)\), Explicit construction of irreducible modules for \(U_q(\mathfrak{gl}_n)\), Quantized Vershik-Kerov theory and quantized central measures on branching graphs

Cites Work

• A Poincaré-Birkhoff-Witt theorem for quantized universal enveloping algebras of type \(A_ N\)
• 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
• Gelfand-Zetlin basis for \(U_ q(\mathfrak{gl}(\text{\textbf{N}}+\text{\textbf{1}}))\) modules.
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