On the degenerate multiplicity of the \(sl_2\) loop algebra for the 6V transfer matrix at roots of unity (Q2495172)
From MaRDI portal
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the degenerate multiplicity of the \(sl_2\) loop algebra for the 6V transfer matrix at roots of unity |
scientific article |
Statements
On the degenerate multiplicity of the \(sl_2\) loop algebra for the 6V transfer matrix at roots of unity (English)
0 references
4 July 2006
0 references
The paper under review starts with introducing the Bethe ansatz equations and regular solutions of them, and defining regular Bethe states. Then the \(\text{sl}_2\) loop algebra symmetry of the \(XXZ\) spin chain at roots of unity is briefly discussed. After this the author explains the Drinfeld realization of the \(\text{sl}_2\) loop algebra and reviews the algorithm for determining the degenerate multiplicity of a regular Bethe state in the sectors. In particular, the dimension of the highest weight representation generated by the regular Bethe state is determined. Finally, some explicit examples of the Drinfeld polynomials are discussed.
0 references
loop algebra
0 references
the six-vertex model
0 references
quantum group
0 references
Drinfeld polynomial
0 references
