๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

The Terwilliger Algebra of a 2-Homogeneous Bipartite Distance-Regular Graph

โœ Scribed by Brian Curtin

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
200 KB
Volume
81
Category
Article
ISSN
0095-8956

No coin nor oath required. For personal study only.

โœฆ Synopsis

Let 1 denote a 2-homogeneous bipartite distance-regular graph with diameter D 3 and valency k 3. Assume that 1 is not isomorphic to a Hamming cube. Fix a vertex x of 1, and let T=T(x) denote the Terwilliger algebra of T with respect to x. We give three sets of generators for T, two of which satisfy the relations of the quantum universal enveloping algebra of the Lie algebra sl(2). We then describe the simple T-modules. We give a pair of canonical bases for each simple T-module, and we give the overlap function for these bases in terms of a basic hypergeometric function. Finally, we give two generators for the center of T.

๐Ÿ“œ SIMILAR VOLUMES

The Local Structure of a Bipartite Dista
The Local Structure of a Bipartite Distance-regular Graph
โœ Brian Curtin ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 285 KB

In this paper, we consider a bipartite distance-regular graph = (X, E) with diameter d โ‰ฅ 3. We investigate the local structure of , focusing on those vertices with distance at most 2 from a given vertex x. To do this, we consider a subalgebra R = R(x) of Mat X (C), where X denotes the set of vertice

On the Multiplicities of the Primitive I
On the Multiplicities of the Primitive Idempotents of a Q-Polynomial Distance-regular Graph
โœ Arlene A Pascasio ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 154 KB

and Terwilliger recently introduced the notion of a tridiagonal pair. We apply their results to distance-regular graphs and obtain the following theorem. THEOREM. Let denote a distance-regular graph with diameter D โ‰ฅ 3. Suppose is Q-polynomial with respect to the ordering E 0 , E 1 , . . . , E D of