The augmented tridiagonal algebra

By Tatsuro Ito, Paul M. Terwilliger. 2009

95 citations recorded by the source corpus.

Motivated by investigations of the tridiagonal pairs of linear transformations, we introduce the augmented tridiagonal algebra ${\mathcal T}_q$. This is an infinite-dimensional associative ${\mathbb C}$-algebra with 1. We classify the finite-dimensional irreducible representations of ${\mathcal T}_q$. All such representations are explicitly constructed via embeddings of ${\mathcal T}_q$ into the $U_q(sl_2)$-loop algebra. As an application, tridiagonal pairs over ${\mathbb C}$ are classified in the case where $q$ is not a root of unity.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d1c3a587c5ebd2b6ed4fd445977f77d4855fce57

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Tatsuro Ito
2. Paul M. Terwilliger
3. Raimundas Vidunas
4. B. Hartwig

In Discrete Mathematics and Combinatorics

1. Tatsuro Ito
2. Paul M. Terwilliger
3. Raimundas Vidunas
4. B. Hartwig

In Geometry and Topology

1. Tatsuro Ito
2. Paul M. Terwilliger
3. Alexei S. Zhedanov
4. Luc Vinet
5. Plamen Iliev
6. 伊藤 達郎

Citations in the corpus

• The Universal Askey-Wilson Algebra (2011, methodology): “Using the alternate presentation we relate ∆ to the q-Onsager algebra [15, Section 4], [34], [55, Definition 3.”
• Tridiagonal pairs of q-Racah type (2008, background): “the shape of A,A∗. The shape conjecture [21, Conjecture 13.5] states that if Fis algebraically closed then ρi ≤ d i for 0 ≤ i ≤ d. The shape conjecture has been proven for a number of special 2 cases [22,24,27,28]. The TD pairA,A∗ is called sharpwhenever ρ 0 = 1. By [45,Theorem 1.3], if Fis algebrai”