Last update: 2 June 2014
This is a typed copy of the LOMI preprint Quantized universal enveloping algebras, the Yang-Baxter equation and invariants of links, I by N.Yu. Reshetikhin.
Recommended for publication by the Scientific Council of Steklov Mathematical Institute, Leningrad Department (LOMI) 6, June, 1987.
All formulae in thin caae are very similar to those in part one of the previous section.
The h.w. of finite dimensional representation of are parametrized by the numbers If is the h.w. vector,
The basic representation of have the h.w. The tensor square of the basic representation is the sum of three irreducible components: and we have the following spectral decomposition of
As in the cases of and one can calculate the matrices and Substituting these matrices into (6.3) we obtain the matrix where This matrix can also be extracted from [Jim1986-2].
The matrices and for any h.w. can be found from the theorems 2. - 3. and from the ramification rule: where
As in the case we have the following propositions.
Proposition 6.1. The algebra is the factor of B.-W. algebra with over the ideal formed by the elements acting nontrivially only in the multipliers of with numbers The elements are defined by (5.11) with the matrix and for
If we consider the block basis in connected with the embedding we obtain the representation of in the block form with the blocks constructed from
Proposition 6.3. The matrices have the following block structure in the basis (6.9): where we use the notations of sections 2 and 5.