Paul Terwilliger

activity

20242026

collaborators

4 papers

math.CO2026

Strengthening the balanced set condition for the distance-regular graph of the bilinear forms

Paul Terwilliger, Jason Williford

We consider a distance-regular graph $Γ = (X, R)$ called the bilinear forms graph $H_{q} (D, N - D)$ ; we assume $N > 2 D \geq 6$ and $q \neq = 2$ . We show that $Γ$ satisfies the followi…

math.CO2025

Raising and lowering maps for tridiagonal pairs

Paul Terwilliger

Let $V$ denote a nonzero finite-dimensional vector space. A tridiagonal pair on $V$ is an ordered pair $A, A^{*}$ of maps in $End (V)$ such that (i) each of $A, A^{*}$ is diagonal…

math.RA2024

The nucleus of the Johnson graph $J (N, D)$

Kazumasa Nomura, Paul Terwilliger

In this paper, we describe the nucleus of the Johnson graph $Γ = J (N, D)$ with $N > 2 D$ . Let $X$ denote the vertex set of $Γ$ . Let $A \in Mat_{X} (C)$ denote the adjace…

math.QA2024

The $S_{3}$ -symmetric $q$ -Onsager algebra and its Lusztig automorphisms

Paul Terwilliger

The $q$ -Onsager algebra $O_{q}$ is defined by two generators and two relations, called the $q$ -Dolan/Grady relations. In 2019, Baseilhac and Kolb introduced two automorphisms of $O_q…

Strengthening the balanced set condition for the distance-regular graph of the bilinear forms

Raising and lowering maps for tridiagonal pairs

The nucleus of the Johnson graph J(N,D)

The S3​-symmetric q-Onsager algebra and its Lusztig automorphisms

The nucleus of the Johnson graph $J (N, D)$

The $S_{3}$ -symmetric $q$ -Onsager algebra and its Lusztig automorphisms