Stephen R Doty

activity

20002023

most citedSchur-Weyl duality for orthogonal groups

37 citations · 93 across the 40 of their papers we have counts for

collaborators

42 papers

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{…

math.CO2021

Doubly stochastic matrices and Schur-Weyl duality for partition algebras

Stephen R. Doty

We prove that the permutations of ${1, \dots, n}$ having an increasing (resp., decreasing) subsequence of length $n - r$ index a subset of the set of all $r$ th Kronecker powers of $…

math.RT2021

Schur--Weyl duality for twin groups

Stephen Doty, Anthony Giaquinto

The twin group $T W_{n}$ on $n$ strands is the group generated by $t_{1}, \dots, t_{n - 1}$ with defining relations $t_{i}^{2} = 1$ , $t_{i} t_{j} = t_{j} t_{i}$ if $∣ i - j ∣ > 1$ . We find a new instance of se…

math.RT2020

Schur-Weyl duality for tensor powers of the Burau representation

Stephen Doty, Anthony Giaquinto

Artin's braid group $B_{n}$ is generated by $σ_{1}, \dots, σ_{n - 1}$ subject to the relations \[ σ_i σ_{i+1} σ_i = σ_{i+1} σ_i σ_{i+1}, \quad σ_iσ_j = σ_j σ_i \text{ if } |i-j|>1. \] Fo…