The partial Temperley-Lieb algebra and its representations

2022/08/08 by Stephen Doty, Doty, Stephen, Anthony Giaquinto +1
Mathematics · #Algebraic structures and combinatorial models #Advanced Combinatorial Mathematics #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2208.04296

Abstract

We give a combinatorial description of a new diagram algebra, the partial Temperley--Lieb algebra, arising as the generic centralizer algebra End_U_q(\mathfrakgl₂)(V^{⊗ k}), where V = V(0) ⊕ V(1) is the direct sum of the trivial and natural module for the quantized enveloping algebra U_q(\mathfrakgl₂). It is a proper subalgebra of the Motzkin algebra (the U_q(\mathfraksl₂)-centralizer) of Benkart and Halverson. We prove a version of Schur--Weyl duality for the new algebras, and describe their generic representation theory.

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