Paul M. Terwilliger

activity

20012026

most citedThe Universal Askey-Wilson Algebra

71 citations · 733 across the 109 of their papers we have counts for

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Showing 2003Show all

14 papers · 1 filter

math.CO2003

The Pseudo Cosine Sequences of a Distance-Regular Graph

Arlene A. Pascasio, Paul Terwilliger

Let $G$ denote a distance-regular graph with diameter $D \geq 3$ , valency $k$ , and intersection numbers $a_{i}$ , $b_{i}$ , $c_{i}$ . By a {\it pseudo cosine sequence} of $G$ we mean a sequen…

math.CO2003

An inequality for regular near polygons

Paul Terwilliger, Chih-wen Weng

Let $G$ denote a near-polygon distance-regular graph with diameter $d \geq 3$ , valency $k$ and intersection numbers $a_{1} > 0$ , $c_{2} > 1$ . Let $θ_{1}$ denote the second largest eigenvalue…

math.QA2003★ 2 cited

Irreducible Modules for the Quantum Affine Algebra $U_{q} (s l^_{2})$ and its Borel subalgebra $U_{q} (s l^_{2})^{\geq 0}$

Georgia Benkart, Paul Terwilliger

Let $U_{q} (s l^_{2})^{\geq 0}$ denote the Borel subalgebra of the quantum affine algebra $U_{q} (s l^_{2})$ . We show that the following hold for any choice of scalars $ε_{0}, ε_{1}$ fro…

math.QA2003

Tridiagonal pairs and the quantum affine algebra $U_{q} (s l^_{2})$

Tatsuro Ito, Paul Terwilliger

Let $K$ denote a field and let $V$ denote a vector space over $K$ with finite positive dimension. By definition a Leonard pair on $V$ is a pair of linear transformations $A : V \to V$ …

math.CO2003

Distance-regular graphs, pseudo primitive idempotents, and the Terwilliger algebra

Paul Terwilliger, Chih-wen Weng

Let $Γ$ denote a distance-regular graph with diameter $D \geq 3$ and Bose-Mesner algebra $M$ . For $θ \in C \cup \infty$ we define a 1 dimensional subspace of $M$ which we call $M (θ)$ .…

math.RA2003★ 2 cited

Two linear transformations each tridiagonal with respect to an eigenbasis of the other; an overview

Paul Terwilliger

Let $K$ denote a field and let $V$ denote a vector space over $K$ with finite positive dimension. We consider an ordered pair of linear transformations $A : V \to V$ and $A^{*} : V \to V$ …

The Pseudo Cosine Sequences of a Distance-Regular Graph

An inequality for regular near polygons

Irreducible Modules for the Quantum Affine Algebra Uq​(sl^2​) and its Borel subalgebra Uq​(sl^2​)≥0

Tridiagonal pairs and the quantum affine algebra Uq​(sl^2​)

Distance-regular graphs, pseudo primitive idempotents, and the Terwilliger algebra

Two linear transformations each tridiagonal with respect to an eigenbasis of the other; an overview

Irreducible Modules for the Quantum Affine Algebra $U_{q} (s l^_{2})$ and its Borel subalgebra $U_{q} (s l^_{2})^{\geq 0}$

Tridiagonal pairs and the quantum affine algebra $U_{q} (s l^_{2})$