Paul M. Terwilliger

activity

20012005

P

-and

Q

-polynomial association schemes

40 citations · 120 across the 22 of their papers we have counts for

collaborators

23 papers

math.RA2005★ 3 cited

Some trace formulae involving the split sequences of a Leonard pair

Kazumasa Nomura, Paul Terwilliger

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

math.CO2005★ 1 cited

Taut distance-regular graphs and the subconstituent algebra

Mark S. MacLean, Paul Terwilliger

We consider a bipartite distance-regular graph $G$ with diameter $D$ at least 4 and valency $k$ at least 3. We obtain upper and lower bounds for the local eigenvalues of $G$ in ter…

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.RA2005

Balanced Leonard Pairs

Kazumasa Nomura, Paul Terwilliger

Let $K$ denote a field and let $V$ denote a vector space over $K$ with finite positive dimension. By a Leonard pair on $V$ we mean an ordered pair of linear transformations $A:V \t…