Tatsuro Ito

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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★ 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

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 $A : V \to V$ …

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

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

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

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

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

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