The Capelli eigenvalue problem for quantum groups

DOI10.1007/s00029-024-01003-8MaRDI QIDQ6657175

Gail Letzter, Hadi Salmasian, Siddhartha Sahi

Publication date: 6 January 2025

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

Mathematics Subject Classification ID

Nonassociative rings and algebras (17-XX) Quantum theory (81-XX)

Cites Work

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• The Capelli problem for \(\mathfrak{gl}(m|n)\) and the spectrum of invariant differential operators
• Quantum symmetric Kac-Moody pairs
• Local finiteness of the adjoint action for quantized enveloping algebras
• Jordan algebras and Capelli identities
• Symmetric and non-symmetric quantum Capelli polynomials
• Quantum symmetric pairs and their zonal spherical functions.
• Orthogonal polynomials associated with root systems
• Interpolation Macdonald polynomials and Cauchy-type identities
• The Capelli identity, tube domains, and the generalized Laplace transform
• Macdonald's symmetric polynomials as zonal spherical functions on some quantum homogeneous spaces
• Symmetric pairs for quantized enveloping algebras
• Quantum zonal spherical functions and Macdonald polynomials
• Some limit transitions between BC type orthogonal polynomials interpreted on quantum complex Grassmannians
• The Capelli eigenvalue problem for Lie superalgebras
• REGULAR FUNCTIONS ON THE SHILOV BOUNDARY
• On a q-analog of a Sahi result
• Classification of bicovariant differential calculi on the quantum groups SLq(n+1) and Spq(2n)
• Separation of Variables for Quantized Enveloping Algebras
• FOCK REPRESENTATIONS AND QUANTUM MATRICES
• Schur 𝑄-functions and the Capelli eigenvalue problem for the Lie superalgebra \ger𝑞(𝑛)
• Invariant differential operators for quantum symmetric spaces
• Weyl algebras for quantum homogeneous spaces

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