论文标题
$ u_q（gl_n）$的张量表示的融合辫子和中心仪
Fused braids and centralisers of tensor representations of $U_q(gl_N)$
论文作者
论文摘要
我们在本文中介绍了融合排列的代数及其变形的融合Hecke代数。第一个是在我们称为融合排列的一组组合对象上定义的，其变形是在我们称为融合辫子的一组拓扑对象上定义的。我们使用这些代数来证明schur-weyl二元定理，用于$ u_q（gl_n）$的自然表示对称能力的任何张量产品。然后，我们继续研究融合的Hecke代数，尤其是我们明确描述了不可约的表示和分支规则。最后，我们的目标是对正在考虑的$ u_q（gl_n）$表示的张量产品的中央汇率描述。我们表现出一个简单的明确元素，我们猜想以从融合的Hecke代数到Centraliser生成内核。在某些情况下，我们证明了这种猜想，尤其是我们获得了$ u_q（SL_2）$的任何有限维表示的任何张量产品的描述。
We present in this paper the algebra of fused permutations and its deformation the fused Hecke algebra. The first one is defined on a set of combinatorial objects that we call fused permutations, and its deformation is defined on a set of topological objects that we call fused braids. We use these algebras to prove a Schur--Weyl duality theorem for any tensor products of any symmetrised powers of the natural representation of $U_q(gl_N)$. Then we proceed to the study of the fused Hecke algebras and in particular, we describe explicitely the irreducible representations and the branching rules. Finally, we aim to an algebraic description of the centralisers of the tensor products of $U_q(gl_N)$-representations under consideration. We exhibit a simple explicit element that we conjecture to generate the kernel from the fused Hecke algebra to the centraliser. We prove this conjecture in some cases and in particular, we obtain a description of the centraliser of any tensor products of any finite-dimensional representations of $U_q(sl_2)$.
