Casimir invariants for quantized affine Lie algebras
نویسندگان
چکیده
منابع مشابه
Quantum Affine Lie Algebras, Casimir Invariants and Diagonalization of the Braid Generator
Let Uq(Ĝ) be an infinite-dimensional quantum affine Lie algebra. A family of central elements or Casimir invariants are constructed and their eigenvalues computed in any integrable irreducible highest weight representation. These eigenvalue formulae are shown to absolutely convergent when the deformation parameter q is such that |q| > 1. It is proven that the universal R-matrix R of Uq(Ĝ) satis...
متن کاملQuantized Affine Lie Algebras and Diagonalization of Braid Generators
Let Uq(Ĝ) be a quantized affine Lie algebra. It is proven that the universal R-matrix R of Uq(Ĝ) satisfies the celebrated conjugation relation R = TR with T the usual twist map. As applications, braid generators are shown to be diagonalizable on arbitrary tensor product modules of integrable irreducible highest weight Uq(Ĝ)-module and a spectral decomposition formula for the braid generators is...
متن کاملRealization of locally extended affine Lie algebras of type $A_1$
Locally extended affine Lie algebras were introduced by Morita and Yoshii in [J. Algebra 301(1) (2006), 59-81] as a natural generalization of extended affine Lie algebras. After that, various generalizations of these Lie algebras have been investigated by others. It is known that a locally extended affine Lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...
متن کاملSymplectic Reflection Algebras and Affine Lie Algebras
These are the notes of my talk at the conference “Double affine Hecke algebras and algebraic geometry” (MIT, May 18, 2010). The goal of this talk is to discuss some results and conjectures suggesting that the representation theory of symplectic reflection algebras for wreath products categorifies certain structures in the representation theory for affine Lie algebras. These conjectures arose fr...
متن کاملInvariants of Triangular Lie Algebras
Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants (‘generalized Casimir operators’) are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so called special upper triangular Lie algebras. Algebraic a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Letters in Mathematical Physics
سال: 1994
ISSN: 0377-9017,1573-0530
DOI: 10.1007/bf00751173