Eigenvalues of quantum Gelfand invariants. (English) Zbl 1543.81140
Summary: We consider the quantum Gelfand invariants which first appeared in a landmark paper by N. Yu. Reshetikhin et al. [Leningr. Math. J. 1, No. 1, 193–225 (1990; Zbl 0715.17015); translation from Algebra Anal. 1, No. 1, 178–206 (1989)]. We calculate the eigenvalues of the invariants acting in irreducible highest weight representations of the quantized enveloping algebra for \(\mathfrak{gl}_n\). The calculation is based on Liouville-type formulas relating two families of central elements in the quantum affine algebras of type \(A\).
©2024 American Institute of Physics
©2024 American Institute of Physics
MSC:
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
| 17B35 | Universal enveloping (super)algebras |
| 17B10 | Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) |
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
Citations:
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