On the Exact Solution of Models based on Non-Standard Representations

Details On the Exact Solution of Models based on Non-Standard Representations On the Exact Solution of Models based on Non-Standard Representations

1999-03-19

arxiv.org/abs/cond-mat/9903300v1

Physics

Condensed Matter

36 pages ReVTeX, no figures

Scientific paper

10.1007/s002200050710

The algebraic Bethe ansatz is a powerful method to diagonalize transfer-matrices of statistical models derived from solutions of (graded) Yang Baxter equations, connected to fundamental representations of Lie (super-)algebras and their quantum deformations respectively. It is, however, very difficult to apply it to models based on higher dimensional representations of these algebras in auxiliary space, which are not of fusion type. A systematic approach to this problem is presented here. It is illustrated by the diagonalization of a transfer-matrix of a model based on the product of two different four-dimensional representations of $U_{q}(\hat{gl}'(2,1;C))$.

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