Publications (85)
Leonard pairs from 24 points of view
Paul Terwilliger
The universal DAHA of type $(C_1^\vee,C_1)$ and Leonard pairs of $q$-Racah type
Kazumasa Nomura, Paul Terwilliger
The split decomposition of a tridiagonal pair
Kazumasa Nomura, Paul Terwilliger
Distance-regular graphs of $q$-Racah type and the $q$-tetrahedron algebra
Tatsuro Ito, Paul Terwilliger
The augmented tridiagonal algebra
Tatsuro Ito, Paul Terwilliger
Towards a classification of the tridiagonal pairs
Kazumasa Nomura, Paul Terwilliger
The Universal Askey-Wilson Algebra and the Equitable Presentation of $U_q(\mathfrak{sl}_2)$
Paul Terwilliger
Distance-regular graphs and the $q$-tetrahedron algebra
Tatsuro Ito, Paul Terwilliger
The Equitable Basis for sl_2
Georgia Benkart, Paul Terwilliger
On the shape of a tridiagonal pair
Kazumasa Nomura, Paul Terwilliger
Affine transformations of a Leonard pair
Kazumasa Nomura, Paul Terwilliger
Distance-regular graphs, pseudo primitive idempotents, and the Terwilliger algebra
Paul Terwilliger, Chih-wen Weng
The switching element for a Leonard pair
Kazumasa Nomura, Paul Terwilliger
Tridiagonal pairs of $q$-Racah type
Tatsuro Ito, Paul Terwilliger
Some trace formulae involving the split sequences of a Leonard pair
Kazumasa Nomura, Paul Terwilliger
The equitable presentation for the quantum group $U_q(g)$ associated with a symmetrizable Kac-Moody algebra $g$
Paul Terwilliger
An inequality for regular near polygons
Paul Terwilliger, Chih-wen Weng
Two linear transformations each tridiagonal with respect to an eigenbasis of the other; comments on the parameter array
Paul Terwilliger
Double Affine Hecke Algebras of Rank 1 and the $Z_3$-Symmetric Askey-Wilson Relations
Tatsuro Ito, Paul Terwilliger
A characterization of Q-polynomial distance-regular graphs
Aleksandar Jurisic, Paul Terwilliger, Arjana Zitnik
Using Catalan words and a $q$-shuffle algebra to describe a PBW basis for the positive part of $U_q({\widehat {\mathfrak{sl}}}_2)$
Paul Terwilliger
A classification of sharp tridiagonal pairs
Tatsuro Ito, Kazumasa Nomura, Paul Terwilliger
The Universal Central Extension of the Three-point sl_2 Loop Algebra
Georgia Benkart, Paul Terwilliger
Tridiagonal pairs of $q$-Racah type and the $μ$-conjecture
Kazumasa Nomura, Paul Terwilliger
The Universal Askey-Wilson Algebra
Paul Terwilliger
The $q$-tetrahedron algebra and its finite dimensional irreducible modules
Tatsuro Ito, Paul Terwilliger
The Tetrahedron algebra, the Onsager algebra, and the $\mathfrak{sl}_2$ loop algebra
Brian Hartwig, Paul Terwilliger
The Lusztig automorphism of the $q$-Onsager algebra
Paul Terwilliger
Finite-dimensional irreducible modules for the three-point $\mathfrak{sl}_2$ loop algebra
Tatsuro Ito, Paul Terwilliger
Krawtchouk polynomials, the Lie algebra $\mathfrak{sl}_2$, and Leonard pairs
Kazumasa Nomura, Paul Terwilliger
Leonard pairs and the Askey-Wilson relations
Paul Terwilliger, Raimundas Vidunas
Tridiagonal pairs of $q$-Racah type, the Bockting operator $Ï$, and $L$-operators for $U_q(L({\mathfrak{sl}}_2))$
Paul Terwilliger
The shape of a tridiagonal pair
Tatsuro Ito, Paul Terwilliger
An algebra generated by two sets of mutually orthogonal idempotents
Tatsuro Ito, Paul Terwilliger
The algebra $U_q({\mathfrak{sl}_2})$ in disguise
Sarah Bockting-Conrad, Paul Terwilliger
Leonard pairs and the q-Racah polynomials
Paul Terwilliger
A poset $Φ_n$ whose maximal chains are in bijection with the $n \times n$ alternating sign matrices
Paul Terwilliger
Tridiagonal matrices with nonnegative entries
Kazumasa Nomura, Paul Terwilliger
Two relations that generalize the $q$-Serre relations and the Dolan-Grady relations
Paul Terwilliger
Finite-dimensional irreducible $U_q(\mathfrak{sl}_2)$-modules from the equitable point of view
Paul Terwilliger
The $q$-Onsager algebra and the positive part of $U_q({\widehat{\mathfrak{sl}}}_2)$
Paul Terwilliger
Self-dual Leonard pairs
Kazumasa Nomura, Paul Terwilliger
Balanced Leonard Pairs
Kazumasa Nomura, Paul Terwilliger
The quantum algebra $U_q(sl_2)$ and its equitable presentation
Tatsuro Ito, Paul Terwilliger, Chih-wen Weng
The A-like matrices for a hypercube
Stefko Miklavic, Paul Terwilliger
Two linear transformations each tridiagonal with respect to an eigenbasis of the other; an overview
Paul Terwilliger
Two linear transformations each tridiagonal with respect to an eigenbasis of the other
Paul Terwilliger
The displacement and split decompositions for a $Q$-polynomial distance-regular graph
Paul Terwilliger
$q$-Inverting pairs of linear transformations and the $q$-tetrahedron algebra
Tatsuro Ito, Paul Terwilliger
The structure of a tridiagonal pair
Kazumasa Nomura, Paul Terwilliger
Transition maps between the 24 bases for a Leonard pair
Kazumasa Nomura, Paul Terwilliger
The Rahman polynomials and the Lie algebra sl_3(C)
Plamen Iliev, Paul Terwilliger
Two linear transformations each tridiagonal with respect to an eigenbasis of the other; an algebraic approach to the Askey scheme of orthogonal polynomials
Paul Terwilliger
The subconstituent algebra of a bipartite distance-regular graph; thin modules with endpoint two
Mark MacLean, Paul Terwilliger
Taut distance-regular graphs and the subconstituent algebra
Mark S. MacLean, Paul Terwilliger
Distance-regular graphs of $q$-Racah type and the universal Askey-Wilson algebra
Paul Terwilliger, Arjana Žitnik
Evaluation modules for the $q$-tetrahedron algebra
Tatsuro Ito, Hjalmar Rosengren, Paul Terwilliger
The Drinfel'd polynomial of a tridiagonal pair
Tatsuro Ito, Paul Terwilliger
The Universal Askey-Wilson Algebra and DAHA of Type $(C_1^{\vee},C_1)$
Paul Terwilliger
An action of the free product $\mathbb Z_2 \star \mathbb Z_2 \star \mathbb Z_2$ on the $q$-Onsager algebra and its current algebra
Paul Terwilliger
The quantum adjacency algebra and subconstituent algebra of a graph
Paul Terwilliger, Arjana Žitnik
Bipartite Q-polynomial distance-regular graphs and uniform posets
Stefko Miklavic, Paul Terwilliger
Two linear transformations each tridiagonal with respect to an eigenbasis of the other; comments on the split decomposition
Paul Terwilliger
Billiard Arrays and finite-dimensional irreducible $U_q(\mathfrak{sl}_2)$-modules
Paul Terwilliger
Mock Tridiagonal Systems
Tatsuro Ito, Paul Terwilliger
Tridiagonal pairs and the quantum affine algebra $U_q({\hat {sl}}_2)$
Tatsuro Ito, Paul Terwilliger
Two non-nilpotent linear transformations that satisfy the cubic $q$-Serre relations
Tatsuro Ito, Paul Terwilliger
Lowering-Raising triples and $U_q(\mathfrak{sl}_2)$
Paul Terwilliger
Totally bipartite tridiagonal pairs
Kazumasa Nomura, Paul Terwilliger
Tight distance-regular graphs
Aleksandar Jurisic, Jack Koolen, Paul Terwilliger
The Lusztig automorphism of $U_q(\mathfrak{sl}_2)$ from the equitable point of view
Paul Terwilliger
Some algebra related to $P$-and $Q$-polynomial association schemes
Tatsuro Ito, Kenichiro Tanabe, Paul Terwilliger
The $q$-Onsager algebra
Tatsuro Ito, Paul Terwilliger
Sharp tridiagonal pairs
Kazumasa Nomura, Paul Terwilliger
Linear transformations that are tridiagonal with respect to both eigenbases of a Leonard pair
Kazumasa Nomura, Paul Terwilliger
Tridiagonal pairs and the $μ$-conjecture
Kazumasa Nomura, Paul Terwilliger
The determinant of $AA^*-A^*A$ for a Leonard pair $A,A^*$
Kazumasa Nomura, Paul Terwilliger
Matrix units associated with the split basis of a Leonard pair
Kazumasa Nomura, Paul Terwilliger
Leonard triples of $q$-Racah type
Paul Terwilliger
Tridiagonal pairs of Krawtchouk type
Tatsuro Ito, Paul Terwilliger
The $q$-Onsager Algebra and the Universal Askey-Wilson Algebra
Paul Terwilliger
The Pseudo Cosine Sequences of a Distance-Regular Graph
Arlene A. Pascasio, Paul Terwilliger
Irreducible Modules for the Quantum Affine Algebra $U_q(\hat{sl}_2)$ and its Borel subalgebra $U_q(\hat{sl}_2)^{\geq 0}$
Georgia Benkart, Paul Terwilliger
Augmented down-up algebras and uniform posets
Paul Terwilliger, Chalermpong Worawannotai
How to sharpen a tridiagonal pair
Tatsuro Ito, Paul Terwilliger