The determinant of \(AA^{*} - A^{*}A\) for a Leonard pair \(A,A^{*}\)

DOI10.1016/j.laa.2005.12.029zbMath1108.15007arXivmath/0511641OpenAlexW2055272396MaRDI QIDQ2496658

Paul M. Terwilliger, Nomura, Kazumasa

Publication date: 20 July 2006

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0511641

zbMATH Keywords

Terwilliger algebracommutatorlinear transformationsAskey schemeq-Racah polynomialirreducible tridiagonal

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Association schemes, strongly regular graphs (05E30) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Linear transformations, semilinear transformations (15A04)

Related Items

Tridiagonal pairs of \(q\)-Racah type, Matrix units associated with the split basis of a Leonard pair, Linear transformations that are tridiagonal with respect to both eigenbases of a Leonard pair, Unnamed Item, Sharp tridiagonal pairs, Towards a classification of the tridiagonal pairs, Tridiagonal pairs of Krawtchouk type, The structure of a tridiagonal pair, The switching element for a Leonard pair, Tridiagonal pairs and the \(\mu \)-conjecture, BIDIAGONAL PAIRS, THE LIE ALGEBRA 𝔰𝔩₂, AND THE QUANTUM GROUP U_q(𝔰𝔩₂), A classification of sharp tridiagonal pairs, Transition maps between the 24 bases for a Leonard pair, Tridiagonal pairs and the \(q\)-tetrahedron algebra, On the shape of a tridiagonal pair

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The subconstituent algebra of an association scheme. I
• The subconstituent algebra of an association scheme. III
• Some trace formulae involving the split sequences of a Leonard pair
• Balanced Leonard pairs
• Normalized Leonard pairs and Askey--Wilson relations
• Leonard pairs from 24 points of view.
• The shape of a tridiagonal pair.
• Leonard pairs and the \(q\)-Racah polynomials
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other; comments on the parameter array
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other: comments on the split decomposition
• Tridiagonal pairs and the Askey--Wilson relations
• On the multiplicities of the primitive idempotents of a \(Q\)-polynomial distance-regular graph
• Introduction to Leonard pairs.
• A family of tridiagonal pairs
• Tridiagonal pairs and the quantum affine algebra \(U_q(\widehat{\text{sl}}_2)\).
• A refinement of the split decomposition of a tridiagonal pair
• Tridiagonal pairs of height one
• The equitable presentation for the quantum group associated with a symmetrizable Kac-Moody algebra
• Three mutually adjacent Leonard 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
• TWO RELATIONS THAT GENERALIZE THE Q-SERRE RELATIONS AND THE DOLAN-GRADY RELATIONS
• TWO NON-NILPOTENT LINEAR TRANSFORMATIONS THAT SATISFY THE CUBIC q-SERRE RELATIONS
• A family of tridiagonal pairs related to the quantum affine algebra U_q(sl_2)
• LEONARD PAIRS AND THE ASKEY–WILSON RELATIONS
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other