Generic Gelfand-Tsetlin modules of quantized and classical orthogonal algebras

DOI10.1016/j.jalgebra.2022.12.019OpenAlexW4313367754MaRDI QIDQ2685350

Jordan Disch

Publication date: 21 February 2023

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.13488

zbMATH Keywords

quantum groupcenterrepresentationinvariantquantummoduleCasimirrationalpatternsalgebraLieclassicalorthogonalquantizedWeylformulasHarish-Chandraquantum symmetric pairGelfand-Tsetlinrationalizedskew group

Mathematics Subject Classification ID

Nonassociative rings and algebras (17-XX)

Cites Work

• Galois orders in skew monoid rings.
• \(q\)-deformed orthogonal and pseudo-orthogonal algebras and their representations
• Capelli identities for classical Lie algebras
• Macdonald's symmetric polynomials as zonal spherical functions on some quantum homogeneous spaces
• Principal Galois orders and Gelfand-Zeitlin modules
• Classification theorem on irreducible representations of the \(q\)-deformed algebra \(U_q^{\prime}(\text{so}_n)\)
• 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
• Serre-Lusztig relations for \(\imath\) quantum groups
• COIDEAL SUBALGEBRAS IN QUANTUM AFFINE ALGEBRAS
• Nonclassical type representations of the \(q\)-deformed algebra \(U_q'(\text{so}_n)\)
• On Gelfand-Zetlin modules over \(U_q(gl_n)\)
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