Irreducible subquotients of generic Gelfand-Tsetlin modules over \(U_q(\mathfrak{gl}_n)\)

DOI10.1016/j.jpaa.2017.11.018zbMath1433.17016arXiv1610.08126OpenAlexW2540384486WikidataQ111288220 ScholiaQ111288220MaRDI QIDQ1748404

Luis Enrique Ramirez, Jian Zhang, Vyacheslav M. Futorny

Publication date: 11 May 2018

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.08126

Mathematics Subject Classification ID

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

Related Items (3)

Admissible representations of simple affine vertex algebras ⋮ Gelfand-Tsetlin modules of quantum \(\mathfrak{gl}_n\) defined by admissible sets of relations ⋮ Explicit construction of irreducible modules for \(U_q(\mathfrak{gl}_n)\)

Cites Work

• The orbit structure of the Gelfand-Zeitlin group on \(n\times n\) matrices
• Singular Gelfand-Tsetlin modules of \(\mathfrak{gl}(n)\)
• On algebraic integrability of Gelfand-Zeitlin fields
• Isomorphism of two realizations of quantum affine algebra \(U_ q(\widehat{\mathfrak{gl}}(n))\)
• Gelfand-Zetlin basis for \(U_ q(\mathfrak{gl}(\text{\textbf{N}}+\text{\textbf{1}}))\) modules.
• Infinite-dimensional representations of the Lie algebra \(\mathfrak{gl}(n,\mathbb C)\) related to complex analogs of the Gelfand-Tsetlin patterns and general hypergeometric functions on the Lie group \(\text{GL}(n,\mathbb C)\).
• Irreducible generic Gelfand-Tsetlin modules of \(\mathfrak{gl}(n)\)
• Irreducible completely pointed modules of quantum groups of type \(A\)
• Construction of Gelfand-Tsetlin basis for \({\mathcal U}_ q(gl(N+1))\)- modules
• Gelfand–Tsetlin Bases for Classical Lie Algebras
• The Gelfand-Zeitlin integrable system and its action on generic elements of gl(n) and so(n)
• ON CERTAIN COMMUTATIVE SUBALGEBRAS OF A UNIVERSAL ENVELOPING ALGEBRA
• The Gelfand–Zeitlin integrable system and K-orbits on the flag variety
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