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- W2950275727 abstract "Let $Omega$ be a vector space over a finite field with q elements. Let G denote the general linear group of endomorphisms of $Omega$ and let us consider the left regular representation $rho: G to B(L_2(X))$ associated to the natural action of G on the set X of linear subspaces of $Omega$. 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." @default.
- W2950275727 created "2019-06-27" @default.
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- W2950275727 date "2004-04-01" @default.
- W2950275727 modified "2023-10-06" @default.
- W2950275727 title "Laplacian operators and Radon transforms on Grassmann graphs" @default.
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