Projective geometries, $Q$-polynomial structures, and quantum groups

Association schemes, strongly regular graphs (05E30) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Quantum groups (quantized function algebras) and their representations (20G42) Projective analytic geometry (51N15)

Related Items (1)

Eigenbasis for a weighted adjacency matrix associated with the projective geometry $B_q (n)$

Cites Work

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Distance-regular graphs
The algebra $U_q(\mathfrak{sl}_2)$ in disguise
Krawtchouk polynomials, the Lie algebra $\mathfrak{sl}_2$, and Leonard pairs
A positive combinatorial formula for the complexity of the $q$-analog of the $n$-cube
The subconstituent algebra of an association scheme. I
The subconstituent algebra of an association scheme. III
The subconstituent algebra of an association scheme. II
A characterization of $Q$-polynomial distance-regular graphs
A duality between pairs of split decompositions for a Q-polynomial distance-regular graph
Distance-regular graphs and the $q$-tetrahedron algebra
A characterization of $P$- and $Q$-polynomial association schemes
A note on thin $P$-polynomial and dual-thin $Q$-polynomial symmetric association schemes
Leonard pairs from 24 points of view.
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
Introduction to Leonard pairs.
Dual polar graphs, the quantum algebra $U_q(\mathfrak{sl}_{2})$, and Leonard systems of dual $q$-Krawtchouk type
Leonard pairs, spin models, and distance-regular graphs
Notes on the Leonard system classification
Algebraic combinatorics. Translated from the Japanese
The displacement and split decompositions for a $Q$-polynomial distance-regular graph
The quantum algebra $U_q(\mathfrak{sl}_2)$ and its equitable presentation
Some matrices associated with the split decomposition for a $Q$-polynomial distance-regular graph
TWO RELATIONS THAT GENERALIZE THE Q-SERRE RELATIONS AND THE DOLAN-GRADY RELATIONS
THE AUGMENTED TRIDIAGONAL ALGEBRA
Orthogonal Polynomials, Duality and Association Schemes
The Lusztig automorphism of Uq(𝔰𝔩2) from the equitable point of view
LEONARD PAIRS AND THE ASKEY–WILSON RELATIONS
Two linear transformations each tridiagonal with respect to an eigenbasis of the other
A $q$-analog of the adjacency matrix of the $n$-cube
A $Q$-polynomial structure associated with the projective geometry $L_N (q)$
A $Q$-polynomial structure for the attenuated space poset $\mathcal{A}_q (N, M)$
Near-bipartite Leonard pairs
Distance-regular graphs, the subconstituent algebra, and the $Q$-polynomial property
On the $Q$-polynomial property of the full bipartite graph of a Hamming graph

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Projective geometries, \(Q\)-polynomial structures, and quantum groups