BGG CATEGORY FOR THE QUANTUM SCHRÖDINGER ALGEBRA

DOI10.1017/S0017089520000166zbMath1495.17010arXiv1904.12468OpenAlexW3106324993MaRDI QIDQ5858947

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Publication date: 15 April 2021

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.12468

zbMATH Keywords

Bernstein-Gelfand-Gelfand (BGG) categoryquantum Schrödinger algebra

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Applications of Lie (super)algebras to physics, etc. (17B81) Quantum groups (quantized function algebras) and their representations (20G42)

Cites Work

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• Category \(\mathcal{O}\) for the Schrödinger algebra
• On wild and tame finite-dimensional Lie algebras
• Quantized symplectic oscillator algebras of rank one
• Lowest weight representations of the Schrödinger algebra and generalized heat/Schrödinger equations
• The prime spectrum of the algebra \(\mathbb{K}_q[X,Y \rtimes U_q(\mathfrak{sl}_2)\) and a classification of simple weight modules]
• Category \(\mathcal O\) for quantum groups
• Classification of simple weight modules with finite-dimensional weight spaces over the Schrödinger algebra
• On simple modules over conformal Galilei algebras
• Aq-Schrödinger algebra, its lowest-weight representations and generalizedq-deformed heat/Schrödinger equations
• Center and Representations of Infinitesimal Hecke Algebras of 𝔰𝔩₂

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