A quantum analogue of the Capelli identity and an elementary differential calculus on \(GL_ q(n)\)

DOI10.1215/S0012-7094-94-07620-5zbMath0835.17013MaRDI QIDQ1345242

Masatoshi Noumi, Tôru Umeda, Masato Wakayama

Publication date: 16 April 1996

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

zbMATH Keywords

commutation relationsdifferential calculusCapelli identityquantum partial derivatives\(q\)-difference operatorsquantum group \(GL_ q (n)\)

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Noncommutative topology (46L85) Noncommutative differential geometry (46L87)

Related Items

Minor identities for quasi-determinants and quantum determinants, A quantum dual pair \(({\mathfrak {sl}}_ 2, {\mathfrak o}_ n)\) and the associated Capelli identity, Matrix Capelli identities related to reflection equation algebra, Quantum immanants and higher Capelli identities, Quantum vector fields via quantum doubles and their applications, Minor summation formula of pfaffians, Minor identities for Sklyanin determinants, Capelli identity on multiparameter quantum linear groups, A quantum deformation of invariants of higher binary forms, A Generalization of the Capelli Identity, Capelli identities for reductive dual pairs, A Cayley-Hamilton theorem for the skew Capelli elements, Quantum \(b\)-functions of prehomogeneous vector spaces of commutative parabolic type, Multiparameter quantum Cauchy-Binet formulas, Unnamed Item, Unnamed Item, Explicit Newton's formula for \({\mathfrak gl}_n\), A nonsymmetric version of Okounkov's BC-type interpolation Macdonald polynomials, On Turnbull identity for skew-symmetric matrices, A quantum shuffle approach to quantum determinants

Cites Work

• Quantum Berezinian and the classical Capelli identity
• Solutions of the Yang-Baxter equation
• 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 \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
• Quantum R matrix for the generalized Toda system
• \((T^*G)_ t\): a toy model for conformal field theory
• Macdonald's symmetric polynomials as zonal spherical functions on some quantum homogeneous spaces
• A \(q\)-analogue of Capelli's identity for \(\text{GL}(2)\)
• Erratum to "Remarks on Classical Invariant Theory"
• Remarks on Classical Invariant Theory
• Symmetric Determinants and the Cayley and Capelli Operator
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