Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 100, 9 pages      arXiv:1009.3476      https://doi.org/10.3842/SIGMA.2010.100
Contribution to the Proceedings of the International Workshop “Recent Advances in Quantum Integrable Systems”

Sklyanin Determinant for Reflection Algebra

Natasha Rozhkovskaya
Department of Mathematics, Kansas State University, USA

Received September 21, 2010, in final form December 23, 2010; Published online December 29, 2010

Abstract
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.

Key words: reflection equation; Sklyanin determinant.

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References

  1. Molev A., Yangians and classical Lie algebras, Mathematical Surveys and Monographs, Vol. 143, American Mathematical Society, Providence, RI, 2007.
  2. Molev A., Yangians and their applications, in Handbook of Algebra, Vol. 3, North-Holland, Amsterdam, 2003, 907-959, math.QA/0211288.
  3. Molev A., Sklyanin determinant, Laplace operators, and charcteristic identities for classical Lie algebras, J. Math. Phys. 36 (1995), 923-943, hep-th/9409036.
  4. Molev A., Nazarov M., Ol'shanskii G., Yangians and classical Lie algebras, Russian Math. Surveys 51 (1996), no. 2, 205-282, hep-th/9409025.
  5. Molev A., Ragoucy E., Representations of reflection algebras, Rev. Math. Phys. 14 (2002), 317-342, math.QA/0107213.
  6. Ol'shanskii G.I., Twisted Yangians and infinite-dimensional classical Lie algebras, in Quantum Groups (Leningrad, 1990), Editor P. Kulish, Lecture Notes in Math., Vol. 1510, Springer, Berlin, 1992, 104-119.
  7. Sklyanin E.K., Boundary conditions for integrable quantum systems, J. Phys. A: Math. Gen. 21 (1988), 2375-2389.

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