Orthogonal Polynomials, Duality and Association Schemes
From MaRDI portal
Publication:3958755
DOI10.1137/0513044zbMath0495.33006OpenAlexW2087651092MaRDI QIDQ3958755
Publication date: 1982
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/0513044
Association schemes, strongly regular graphs (05E30) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05)
Related Items
A bivariate \(Q\)-polynomial structure for the non-binary Johnson scheme ⋮ Duality and difference operators for matrix valued discrete polynomials on the nonnegative integers ⋮ Near-bipartite Leonard pairs ⋮ Introduction to Leonard pairs. ⋮ Algebraic Heun operator and band-time limiting ⋮ Tridiagonal pairs and the quantum affine algebra \(U_q(\widehat{\text{sl}}_2)\). ⋮ An elementary approach to \(6j\)-symbols (classical, quantum, rational, trigonometric, and elliptic) ⋮ Tridiagonal pairs of \(q\)-Racah type ⋮ Hypergeometric orthogonal polynomials with respect to Newtonian bases ⋮ From superintegrability to tridiagonal representation of \(\beta \)-ensembles ⋮ Anticodes for the Grassmann and bilinear forms graphs ⋮ On classical orthogonal polynomials ⋮ (𝑛+1,𝑚+1)-hypergeometric functions associated to character algebras ⋮ Association schemes and quadratic transformations for orthogonal polynomials ⋮ Rational functions and association scheme parameters ⋮ Elliptic Racah polynomials ⋮ Zeros and orthogonality of the Askey-Wilson polynomials for \(q\) a root of unity ⋮ Compatibility and companions for Leonard pairs ⋮ The association schemes of dual polar spaces of type \(^ 2A_{2d- 1}(p^ f)\) are characterized by their parameters if \(d\geq 3\) ⋮ The \(q\)-version of a theorem of Bochner ⋮ The \(Q\)-polynomial idempotents of a distance-regular graph ⋮ Parallelogram-free distance-regular graphs ⋮ The Terwilliger algebra of symplectic dual polar graphs, the subspace lattices and \(U_q(\mathrm{sl}_2)\) ⋮ Circular bidiagonal pairs ⋮ Para-Bannai-Ito polynomials ⋮ Matrix elements of SO(3) in sl3 representations as bispectral multivariate functions ⋮ A \(Q\)-polynomial structure associated with the projective geometry \(L_N (q)\) ⋮ Krawtchouk polynomials, the Lie algebra \(\mathfrak{sl}_2\), and Leonard pairs ⋮ Unnamed Item ⋮ Leonard pairs from 24 points of view. ⋮ Exceptional Charlier and Hermite orthogonal polynomials ⋮ The shape of a tridiagonal pair. ⋮ Sharp tridiagonal pairs ⋮ Dualities in the q‐Askey Scheme and Degenerate DAHA ⋮ An explicit example of polynomials orthogonal on the unit circle with a dense point spectrum generated by a geometric distribution ⋮ Towards a classification of the tridiagonal pairs ⋮ A linear map acts as a Leonard pair with each of the generators of \(U(s l_2)\) ⋮ Non-symmetric, metric, cometric association schemes are self-dual ⋮ A new approach to the theory of classical hypergeometric polynomials ⋮ Constructing bispectral dual Hahn polynomials ⋮ Signal Processing, Orthogonal Polynomials, and Heun Equations ⋮ An algebraic description of the bispectrality of the biorthogonal rational functions of Hahn type ⋮ Leonard triples, the Racah algebra, and some distance-regular graphs of Racah type ⋮ Leonard triples from the equitable basis of \(sl_2\) ⋮ On Lee association schemes over \(\mathbb{Z}_4\) and their Terwilliger algebra ⋮ Leonard triples of \(q\)-Racah type and their pseudo intertwiners ⋮ Nonsymmetric Askey-Wilson polynomials and \(Q\)-polynomial distance-regular graphs ⋮ The structure of a tridiagonal pair ⋮ Dual $-1$ Hahn polynomials: “Classical” polynomials beyond the Leonard duality ⋮ On the Askey-Wilson polynomials ⋮ Cyclic tridiagonal pairs, higher order Onsager algebras and orthogonal polynomials ⋮ The subconstituent algebra of an association scheme. I ⋮ Generalized Bochner theorem: Characterization of the Askey-Wilson polynomials ⋮ Askey-Wilson polynomials, kernel polynomials and association schemes ⋮ Designs as maximum codes in polynomial metric spaces ⋮ BIDIAGONAL PAIRS, THE LIE ALGEBRA 𝔰𝔩2, AND THE QUANTUM GROUP Uq(𝔰𝔩2) ⋮ LEONARD PAIRS AND THE ASKEY–WILSON RELATIONS ⋮ Exactly solvable birth and death processes ⋮ Two linear transformations each tridiagonal with respect to an eigenbasis of the other; comments on the parameter array ⋮ A classification of sharp tridiagonal pairs ⋮ Two linear transformations each tridiagonal with respect to an eigenbasis of the other ⋮ Two linear transformations each tridiagonal with respect to an eigenbasis of the other: comments on the split decomposition ⋮ Exceptional Meixner and Laguerre orthogonal polynomials ⋮ TWO NON-NILPOTENT LINEAR TRANSFORMATIONS THAT SATISFY THE CUBIC q-SERRE RELATIONS ⋮ On some recent progress in the classification of (\(P\) and \(Q\))-polynomial association schemes ⋮ Dual polar graphs, a nil-DAHA of rank one, and non-symmetric dual \(q\)-Krawtchouk polynomials ⋮ Dual polar graphs, a nil-DAHA of rank one, and non-symmetric dual \(q\)-Krawtchouk polynomials ⋮ TD-pairs and the $q$-Onsager algebra ⋮ Exceptional Hahn and Jacobi orthogonal polynomials ⋮ A bilinear form relating two Leonard systems ⋮ The Norton algebra of a \(Q\)-polynomial distance-regular graph ⋮ The attenuated space poset \(\mathcal{A}_q(N, M)\) ⋮ On upper bounds for code distance and covering radius of designs in polynomial metric spaces ⋮ Notes on the Leonard system classification ⋮ Finite-dimensional irreducible modules of the universal Askey-Wilson algebra ⋮ Directed distance regular graphs with the Q-polynomial property ⋮ The non-symmetric Wilson polynomials are the Bannai–Ito polynomials ⋮ Scaling limits for the Gibbs states on distance-regular graphs with classical parameters ⋮ The graphs G(n,k) of the Johnson schemes are unique for n\(\geq 20\) ⋮ Discrete Time-Band Limiting Operators and Commuting Tridiagonal Matrices ⋮ Dunkl shift operators and Bannai-Ito polynomials ⋮ Energy bounds for codes in polynomial metric spaces ⋮ Commutative association schemes ⋮ New examples of Krall-Meixner and Krall-Hahn polynomials, with applications to the construction of exceptional Meixner and Laguerre polynomials ⋮ A limit $q=-1$ for the big $q$-Jacobi polynomials ⋮ Orthogonality of Racah and Wilson polynomials ⋮ On the shape of a tridiagonal pair ⋮ Higher order recurrence relation for exceptional Charlier, Meixner, Hermite and Laguerre orthogonal polynomials ⋮ Circular Hessenberg pairs ⋮ Two linear transformations each tridiagonal with respect to an eigenbasis of the other; the TD-D canonical form and the LB-UB canonical form ⋮ Bispectral dual Hahn polynomials with an arbitrary number of continuous parameters ⋮ Orthogonal polynomials from Hermitian matrices ⋮ Parameters of association schemes that are both P- and Q-polynomial ⋮ The factorization method for the Askey-Wilson polynomials ⋮ Almost 2-homogeneous bipartite distance-regular graphs ⋮ Unified theory of exactly and quasiexactly solvable “discrete” quantum mechanics. I. Formalism ⋮ The universal DAHA of type (C1∨,C1) and Leonard triples ⋮ The Terwilliger algebra of a 2-homogeneous bipartite distance-regular graph ⋮ Bipartite \(Q\)-polynomial quotients of antipodal distance-regular graphs ⋮ Orthogonal polynomials from Hermitian matrices. II ⋮ The classification of distance-regular graphs of type IIB ⋮ A class of distance-regular graphs that are \(\phi\)-polynomial
