The Terwilliger Algebra of the Hypercube

✍ Scribed by Junie T Go

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 285 KB
• Volume: 23
• Category: Article
• ISSN: 0195-6698
• DOI: 10.1006/eujc.2000.0514

✦ Synopsis

Using the above equations, we find the irreducible T -modules. For each irreducible T -module W , we display two orthogonal bases, which we call the standard basis and the dual standard basis. We describe the action of A and A * on each of these bases. We give the transition matrix from the standard basis to the dual standard basis for W . We compute the multiplicity with which each irreducible T -module W appears in C X . We give an elementary proof that Q D has the Q-polynomial property. We show that T is a homomorphic image of the universal enveloping algebra of the Lie algebra sl 2 (C). We obtain an element φ of T that generates the center of T . We obtain the central primitive idempotents of T as polynomials in φ.