A quantum dual pair \(({\mathfrak {sl}}_ 2, {\mathfrak o}_ n)\) and the associated Capelli identity

DOI10.1007/BF00739369zbMath0842.17020MaRDI QIDQ1900437

Masatoshi Noumi, Tôru Umeda, Masato Wakayama

Publication date: 31 October 1995

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

zbMATH Keywords

\(q\)-deformationoscillator representationCapelli identityquantum dual pair

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)

Related Items (5)

COIDEAL SUBALGEBRAS IN QUANTUM AFFINE ALGEBRAS ⋮ Unnamed Item ⋮ Unnamed Item ⋮ New Schur function series ⋮ Geometric Howe dualities of finite type

Cites Work

• Quantum Berezinian and the classical Capelli identity
• The Capelli identity, the double commutant theorem, and multiplicity-free actions
• Q-analogues of Clifford and Weyl algebras - spinor and oscillator representations of quantum enveloping algebras
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
• \(q\)-deformed orthogonal and pseudo-orthogonal algebras and their representations
• A quantum analogue of the Capelli identity and an elementary differential calculus on \(GL_ q(n)\)
• A \(q\)-analogue of Capelli's identity for \(\text{GL}(2)\)
• Remarks on Classical Invariant Theory
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