Orthogonal basis for the Shapovalov form on $U_q(\mathfrak{sl}(n + 1))$

DOI10.1142/S0129055X1550004XzbMath1394.17040arXiv1206.3647MaRDI QIDQ5255193

Andrey Mudrov

Publication date: 12 June 2015

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

Full work available at URL: https://arxiv.org/abs/1206.3647

zbMATH Keywords

Verma modulesorthogonal basisShapovalov form

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

Related Items (6)

On representations of quantum conjugacy classes of \(\mathrm{GL}(n)\) ⋮ Branching rules for finite-dimensional \(\mathcal {U}_{q}(\mathfrak {su}(3))\)-representations with respect to a right coideal subalgebra ⋮ Shapovalov elements and Hasse diagrams ⋮ Shapovalov elements of classical and quantum groups ⋮ Regularization of Mickelsson generators for nonexceptional quantum groups ⋮ Quantum twistors

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Irreducible highest weight modules and equivariant quantization
• Inverting the Shapovalov form
• Kontravariante Formen auf induzierten Darstellungen halbeinfacher Lie-Algebren
• Representations of affine Lie algebras, parabolic differential equations, and Lamé functions
• Step algebras of semi-simple subalgebras of Lie algebras
• Canonical factorization of continuous operator functions relative to the circle
• Invariant *-products on coadjoint orbits and the Shapovalov pairing
• Gelfand–Tsetlin Bases for Classical Lie Algebras
• Projection operators for simple lie groups

This page was built for publication: Orthogonal basis for the Shapovalov form on $U_q(\mathfrak{sl}(n + 1))$