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The Subconstituent Algebra of an Association Scheme, (Part I)
AbstractWe introduce a method for studying commutative association schemes with “many” vanishing intersection numbers and/or Krein parameters, and apply the method to the P- and Q-polynomial schemes.Expand
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Two linear transformations each tridiagonal with respect to an eigenbasis of the other; an overview
Let $K$ denote a field and let $V$ denote a vector space over $K$ with finite positive dimension. We consider an ordered pair of linear transformations $A:V\to V$ and $A^*:V\to V$ that satisfyExpand
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Some algebra related to P- and Q-polynomial association schemes
TLDR
We introduce a mild generalization of a Leonard pair called a tridiagonal pair such that for each transformation all eigenspaces have dimension one. Expand
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The Universal Askey-Wilson Algebra
In 1992 A. Zhedanov introduced the Askey-Wilson algebra AW=AW(3) and used it to describe the Askey-Wilson polynomials. In this paper we introduce a central extension $\Delta$ of AW, obtained from AWExpand
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The quantum algebra Uq(sl2) and its equitable presentation
Abstract We show that the quantum algebra U q ( sl 2 ) has a presentation with generators x ± 1 , y , z and relations x x −1 = x −1 x = 1 , q x y − q −1 y x q − q −1 = 1 , q y z − q −1 z y q − q −1 =Expand
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Kite-free distance-regular graphs
TLDR
We show that the Hermitean forms graph Her ( d , q ) is uniquely determined by its intersection numbers if d ≥ 3. Expand
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The Incidence Algebra of a Uniform Poset
Let P,≤ denote a finite graded poset of rank N ≥ 2, with fibers P 0, P 1, ... , P N. Let the matrices L i, R i, E i * (0 ≤ i ≤ N) have rows and columns indexed by P, and entries $$Expand
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Tridiagonal pairs and the quantum affine algebra Uq(sl2) (代数的組合せ論)
Let K denote an algebraically closed field and let q denote a nonzero scalar in K that is not a root of unity. Let V denote a vector space over K with finite positive dimension and let A, A∗ denote aExpand
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The Tetrahedron algebra, the Onsager algebra, and the sl2 loop algebra
Let K denote a field with characteristic 0 and let T denote an indeterminate. We give a presentation for the three-point loop algebra sl2⊗K[T,T−1,(T−1)−1] via generators and relations. ThisExpand
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Distance-regular graphs with girth 3 or 4: I
TLDR
We study the structure of a distance-regular graph Γ with girth 3 or 4. Expand
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