Laplacian operators and Radon transforms on Grassmann graphs
| dc.creator | Marco, J. M. | |
| dc.creator | Parcet, J. | |
| dc.date | 2004-04-01 | |
| dc.date | 2005-08-26 | |
| dc.date.accessioned | 2026-07-07T05:06:59Z | |
| dc.date.available | 2026-07-07T05:06:59Z | |
| dc.description | Let $Ω$ be a vector space over a finite field with q elements. Let G denote the general linear group of endomorphisms of $Ω$ and let us consider the left regular representation $ρ: G \to B(L_2(X))$ associated to the natural action of G on the set X of linear subspaces of $Ω$. In this paper we study a natural basis B of the algebra $End_{G}(L_2(X))$ of intertwining maps on $L_2(X)$. By using a Laplacian operator on Grassmann graphs, we identify the kernels in B as solutions of a basic hypergeometric difference equation. This provides two expressions for these kernels. One in terms of the q-Hahn polynomials and the other by means of a Rodrigues type formula. Finally, we obtain a useful product formula for the mappings in B. We give two different proofs. One uses the theory of classical hypergeometric polynomials and the other is supported by a characterization of spherical functions in finite symmetric spaces. Both proofs require the use of certain associated Radon transforms. | |
| dc.description | 32 pages | |
| dc.identifier | https://arxiv.org/abs/math/0404019 | |
| dc.identifier | http://arxiv.org/abs/math/0404019 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70682 | |
| dc.subject | Combinatorics | |
| dc.subject | Representation Theory | |
| dc.subject | 05A30; 05E30; 20G40 | |
| dc.title | Laplacian operators and Radon transforms on Grassmann graphs | |
| dc.type | text |