Yangians and Classical Lie Algebras, Part II. Sklyanin determinant, Laplace operators and characteristic identities

1994/09/07 by Alexander Molev, Molev, Alexander
Chemistry · Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Molecular spectroscopy and chirality #hep-th

paper · pdf · doi:10.48550/arxiv.hep-th/9409036

37 pages, AmSTeX

arxiv created 1994/09/07 · openalex publication_date 1994/09/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the structure of quantized enveloping algebras called twisted Yangians, which are naturally associated with the B, C, and D series of the classical Lie algebras. We obtain an explicit formula for the formal series (the Sklyanin determinant) whose coefficients are free generators of the center of the twisted Yangian. As a corollary we obtain a new system of algebraically independent generators of the center of the universal enveloping algebra for the orthogonal and symplectic Lie algebras and find the characteristic polynomial for the matrix formed by the generators of these Lie algebras.

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