Sklyanin Determinant for Reflection Algebra
نویسندگان
چکیده
Reflection algebras is a class of algebras associated with integrable models with boundaries. The coefficients of Sklyanin determinant generate the center of the reflection algebra. We give a combinatorial description of Sklyanin determinant suitable for explicit computations.
منابع مشابه
Topics in Hidden Symmetries. Iv.
This note being devoted to some aspects of the inverse problem of representation theory explicates the links between researches on the Sklyanin algebras and the author’s (based on the noncommutative geometry) approach to the setting free of hidden symmetries in terms of ”the quantization of constants”. Namely, the Racah–Wigner algebra for the Sklyanin algebra is constructed. It may be considere...
متن کاملPainlevé VI , Rigid Tops and Reflection Equation
We show that the Painlevé VI equation has an equivalent form of the non-autonomous Zhukovsky-Volterra gyrostat. This system is a generalization of the Euler top in C 3 and include the additional constant gyrostat momentum. The quantization of its autonomous version is achieved by the reflection equation. The corresponding quadratic algebra generalizes the Sklyanin algebra. As by product we defi...
متن کاملNoncommutative Symmetric Functions and Laplace Operators for Classical Lie Algebras
New systems of Laplace (Casimir) operators for the orthogonal and symplectic Lie algebras are constructed. The operators are expressed in terms of paths in graphs related to matrices formed by the generators of these Lie algebras with the use of some properties of the noncommutative symmetric functions associated with a matrix. The decomposition of the Sklyanin determinant into a product of qua...
متن کاملDegenerate Sklyanin Algebras and Generalized Twisted Homogeneous Coordinate Rings
In this work, we introduce the point parameter ring B, a generalized twisted homogeneous coordinate ring associated to a degenerate version of the three-dimensional Sklyanin algebra. The surprising geometry of these algebras yields an analogue to a result of Artin-Tatevan den Bergh, namely that B is generated in degree one and thus is a factor of the corresponding degenerate Sklyanin algebra.
متن کاملSklyanin Invariant Integration
The Sklyanin algebra admits realizations by difference operators acting on theta functions. Sklyanin found an invariant metric for the action and conjectured an explicit formula for the corresponding reproducing kernel. We prove this conjecture, and also give natural biorthogonal and orthogonal bases for the representation space. Moreover, we discuss connections with elliptic hypergeometric ser...
متن کامل