Dilute Algebras and Solvable Lattice Models

Abstract

The definition of a dilute braid-monoid algebra is briefly reviewed. The construction of solvable vertex and interaction-round-a-face models built on representations of the dilute Temperley-Lieb and Birman-Wenzl-Murakami algebras is discussed.

8 pages, uuencoded gz-compressed PostScript, to appear in the proceedings of the satellite meeting of STATPHYS 19, `Statistical Models, Yang-Baxter Equation and Related Topics', August 8-10, 1995, Tianjin, China

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• The principal indecomposable modules of the dilute Temperley-Lieb algebra
• The Bubble Algebra: Structure of a Two-Colour Temperley-Lieb Algebra
• $U_q({\mathfrak{sl}}_n)$ web models and ${\mathbb{Z}}_n$ spin interfaces
• Dilute oriented loop models
• Currents in the dilute $O(n=1)$ model