A. Giaquinto

activity

19932026

most citedGraphs, Frobenius functionals, and the classical Yang-Baxter equation

22 citations · 82 across the 27 of their papers we have counts for

collaborators

29 papers

math.RT2026

Fence Posets, Good Gradings and Frobenius Maximal Parabolics

Anthony Giaquinto, John Irving, Aaron Lauve +1

Let $L$ be a Frobenius maximal parabolic subalgebra of $sl_{n}$ . For any $F \in L^{*}$ for which the Kirillov form $B_{F} (x, y) = F ([x, y])$ is non-degenerate, l…

math.QA2026

The Center of the Temperley-Lieb Algebra

Anthony Giaquinto, Mitja Mastnak

We compute the dimension of the center of the Temperley--Lieb algebra $T L_{n} (δ)$ over a field of characteristic zero for every nonzero value of the parameter $δ$ . The…

math.QA2025

Lowering operators, orthogonal decomposition of tensor space, and quantized Schur--Weyl duality

Stephen Doty, Anthony Giaquinto, Stuart Martin

For $q$ generic, Jimbo showed that $q$ -tensor space $V_{q}^{\otimes r}$ (where $V_{q}$ is the $n$ -dimensional vector representation) satisfies Schur--Weyl duality with respect to the c…

math.CO2023

Origins of the Temperley-Lieb algebra: early history

Stephen Doty, Anthony Giaquinto

We give an historical survey of some of the original basic algebraic and combinatorial results on Temperley-Lieb algebras, with a focus on certain results that have become folklore…

math.RT2023

An orthogonal realization of representations of the Temperley-Lieb algebra

Stephen Doty, Anthony Giaquinto

Under a suitable hypothesis, we construct a full set of pairwise orthogonal maximal vectors in $V^{\otimes n}$ , where $V = V (1)$ is the simple module of highest weight $1$ for the qu…

math.RT2022

The partial Temperley-Lieb algebra and its representations

Stephen Doty, Anthony Giaquinto

We give a combinatorial description of a new diagram algebra, the partial Temperley--Lieb algebra, arising as the generic centralizer algebra $\mathrm{End}_{\mathbf{U}_q(\mathfrak{…