Paul Terwilliger

activity

20032005

P

-and

Q

-polynomial association schemes

40 citations · 121 across the 23 of their papers we have counts for

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8 papers · 1 filter

math.QA2005

Two non-nilpotent linear transformations that satisfy the cubic $q$ -Serre relations

Tatsuro Ito, Paul Terwilliger

Let $K$ denote an algebraically closed field with characteristic 0, and let $q$ denote a nonzero scalar in $K$ that is not a root of unity. Let $A_{q}$ denote the unital associative…

math.QA2005★ 12 cited

The equitable presentation for the quantum group $U_{q} (g)$ associated with a symmetrizable Kac-Moody algebra $g$

Paul Terwilliger

We consider the quantum group $U_{q} (g)$ associated with a symmetrizable Kac-Moody algebra $g$ . We display a presentation for $U_{q} (g)$ that we find attractive; we call this the equit…

math.QA2005★ 17 cited

The quantum algebra $U_{q} (s l_{2})$ and its equitable presentation

Tatsuro Ito, Paul Terwilliger, Chih-wen Weng

We show that the quantum algebra $U_{q} (s l_{2})$ has a presentation with generators $x, x^{- 1}, y, z$ and relations $x x^{- 1} = 1$ , $x^{- 1} x = 1$ , $\frac{q x y - q ^{- 1} y x}{q - q ^{- 1}} = 1$ , $\frac{q…

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.QA2003★ 14 cited

Two relations that generalize the $q$ -Serre relations and the Dolan-Grady relations

Paul Terwilliger

We define an algebra on two generators which we call the Tridiagonal algebra, and we consider its irreducible modules. The algebra is defined as follows. Let K denote a field, and…

Two non-nilpotent linear transformations that satisfy the cubic q-Serre relations

The equitable presentation for the quantum group Uq​(g) associated with a symmetrizable Kac-Moody algebra g

The quantum algebra Uq​(sl2​) and its equitable presentation

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​)

Two relations that generalize the q-Serre relations and the Dolan-Grady relations

Two non-nilpotent linear transformations that satisfy the cubic $q$ -Serre relations

The equitable presentation for the quantum group $U_{q} (g)$ associated with a symmetrizable Kac-Moody algebra $g$

The quantum algebra $U_{q} (s l_{2})$ and its equitable presentation

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 $U_{q} (s l^_{2})$

Two relations that generalize the $q$ -Serre relations and the Dolan-Grady relations