Terwilliger algebras of wreath products of association schemes
نویسندگان
چکیده
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi CHAPTER 1. A GENERAL OVERVIEW AND INTRODUCTION . . . . 1 CHAPTER 2. PRELIMINARIES: COMMUTATIVE ASSOCIATION SCHEMES AND THEIR TERWILLIGER ALGEBRAS . . . . . . . . . . . . . . . . . 4 2.1 The Bose-Mesner Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 The Dual Bose-Mesner Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 The Terwilliger Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3.1 The Central Primitive Idempotents of T . . . . . . . . . . . . . . . . . . 8 2.3.2 Some Triple Products in the Terwilliger Algebra . . . . . . . . . . . . . 9 CHAPTER 3. WREATH PRODUCTS OF ONE-CLASS ASSOCIATION SCHEMES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.1 The Wreath Product of Association Schemes . . . . . . . . . . . . . . . . . . . 10 3.2 The D-class Association Scheme Kn1 oKn2 o · · · oKnD . . . . . . . . . . . . . . 11 3.3 The Dimension of the T -algebra of Kn1 oKn2 o · · · oKnD . . . . . . . . . . . . . 13 3.4 Building the basis of D copies from D − 1 copies of Kni . . . . . . . . . . . . . 20 CHAPTER 4. STRUCTURE OF TERWILLIGER ALGEBRAS OF WREATH POWERS OF ONE-CLASS ASSOCIATION SCHEMES . . . . . . . . . . 23 4.1 The Terwilliger Algebra of Km . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.2 The Scheme Km oKm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.3 The Terwilliger Algebra of (Km) . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.3.1 The Scheme (Km) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
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Terwilliger algebras of wreath products of one-class association schemes
In this paper, we study the wreath product of one-class association schemes Kn =H(1, n) for n≥ 2. We show that the d-class association scheme Kn1 Kn2 · · · Knd formed by taking the wreath product of Kni (for ni ≥ 2) has the triple-regularity property. Then based on this fact, we determine the structure of the Terwilliger algebra of Kn1 Kn2 · · · Knd by studying its irreducible modules. In parti...
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