The partial Temperley–Lieb algebra and its representations
Stephen Doty
Loyola University Chicago, USAAnthony Giaquinto
Loyola University Chicago, USA
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Abstract
In this paper, we give a combinatorial description of a new diagram algebra, the partial Temperley–Lieb algebra, arising as the generic centralizer algebra , where is the direct sum of the trivial and natural module for the quantized enveloping algebra . It is a proper subalgebra of the Motzkin algebra (the -centralizer) of Benkart and Halverson. We prove a version of Schur–Weyl duality for the new algebras, and describe their generic representation theory.
Cite this article
Stephen Doty, Anthony Giaquinto, The partial Temperley–Lieb algebra and its representations. J. Comb. Algebra 7 (2023), no. 3/4, pp. 401–439
DOI 10.4171/JCA/74