Noncommutative symmetric functions and Laplace operators for classical Lie algebras

DOI10.1007/BF00750763zbMath0843.17003arXivhep-th/9409090MaRDI QIDQ1900497

Alexander I. Molev

Publication date: 29 November 1995

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

Full work available at URL: https://arxiv.org/abs/hep-th/9409090

zbMATH Keywords

Casimir operatorsnoncommutative symmetric functionsquasi-determinantssymplectic Lie algebrasLaplace operatorsSklyanin determinantquantum determinant

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Universal enveloping (super)algebras (17B35)

Related Items

Unnamed Item ⋮ Symmetric functions, noncommutative symmetric functions and quasisymmetric functions. II. ⋮ Generalized symmetrization in enveloping algebras ⋮ Stirling partitions of the symmetric group and Laplace operators for the orthogonal Lie algebra ⋮ A note on constructing quasi modules for quantum vertex algebras from twisted Yangians ⋮ Acyclic complexes related to noncommutative symmetric functions ⋮ Quasideterminants ⋮ Witt vectors. Part 1 ⋮ Finite-dimensional irreducible representations of twisted Yangians ⋮ Zassenhaus Lie idempotents, \(q\)-bracketing and a new exponential/logarithm correspondence

Cites Work

• Quantum Berezinian and the classical Capelli identity
• The Capelli identity, the double commutant theorem, and multiplicity-free actions
• Pseudocharacters on the group \(\text{SL}(2,\mathbb{Z})\)
• Noncommutative symmetric functions
• Determinants of matrices over noncommutative rings
• Minor identities for quasi-determinants and quantum determinants