论文标题
两个边界temberley-lieb代数的校准表示形式
Calibrated representations of two boundary Temperley-Lieb algebras
论文作者
论文摘要
两个边界temberley-lieb代数$ tl_k $在统计力学中的晶格模型的传输矩阵公式中出现，尤其是在引入六个Vertex模型的可集成边界项中。在本文中，我们对校准的表示形式进行了分类和研究 - 所有墨菲元素（积分）同时对角线的表示形式 - 反过来又对应于相关模型中的转移矩阵。我们的方法建立在实现$ tl_k $的基础上，作为类型$ c_k $ affine hecke algebra $ h_k $的商的商。在以前的工作中，我们通过编织图，张量空间操作员和相关组合结构来研究此Hecke代数。本文在本文中直接应用，以提供组合分类和构建所有不可约定的校准$ tl_k $ - 模块，并解释这些模块如何由量子组$ u_q \ mathfrak {gl} _2 $ a schur-weyl二元性产生。
The two boundary Temperley-Lieb algebra $TL_k$ arises in the transfer matrix formulation of lattice models in Statistical Mechanics, in particular in the introduction of integrable boundary terms to the six-vertex model. In this paper, we classify and study the calibrated representations---those for which all the Murphy elements (integrals) are simultaneously diagonalizable---which, in turn, corresponds to diagonalizing the transfer matrix in the associated model. Our approach is founded upon the realization of $TL_k$ as a quotient of the type $C_k$ affine Hecke algebra $H_k$. In previous work, we studied this Hecke algebra via its presentation by braid diagrams, tensor space operators, and related combinatorial constructions. That work is directly applied herein to give a combinatorial classification and construction of all irreducible calibrated $TL_k$-modules and explain how these modules also arise from a Schur-Weyl duality with the quantum group $U_q\mathfrak{gl}_2$.
