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Palabra: GRASSMANN MANIFOLDS (Palabras)
2 registros cumplieron la condición especificada en la base de información BIBCYT. ()
Registro 1 de 2, Base de información BIBCYT
Publicación seriada
Referencias AnalíticasReferencias Analíticas
Autor: Prasad, Gopal ; Yeung, Sai-Kee
Título: Arithmetic fake projective spaces and arithmetic fake Grassmannians
Páginas/Colación: pp. 379-407
Fecha: March 2009
American Journal of Mathematics Vol. 131, no. 2 April 2009
Información de existenciaInformación de existencia

Palabras Claves: Palabras: GRASSMANN MANIFOLDS GRASSMANN MANIFOLDS, Palabras: PROJECTIVE SPACES PROJECTIVE SPACES

Resumen
In a recent paper we have classified fake projective planes

In a recent paper we have classified fake projective planes. Natural higher dimensional generalization of these surfaces are arithmetic fake Pcn-1, and arithmetic fake Grm,n. In this paper we show that arithmetic fake Pcn-1 can exist only if n = 3, 5, and an arithmetic fake Grm,n can exist, with n > 3 odd, only if n = 5. Here we construct four distinct arithmetic fake Pc4, and four distinct fake arithmetic Gr2,5. Furthermore, we use certain results and computations of [PY] to exhibit five irreducible arithmetic fake Pc2. All these are connected smooth (complex projective) Shimura varieties.

Registro 2 de 2, Base de información BIBCYT
Publicación seriada
Referencias AnalíticasReferencias Analíticas
Autor: Zhang , Genkai
Título: Radon transform on symmetric matrix domains
Páginas/Colación: pp. 1351-1369
Fecha: March 2009
Transactions of the American Mathematical Society Vol. 361, no.3 March 2009
Información de existenciaInformación de existencia

Palabras Claves: Palabras: BERNSTEIN-SATO FORMULA BERNSTEIN-SATO FORMULA, Palabras: CHEREDNIK OPERATORS CHEREDNIK OPERATORS, Palabras: FRACTIONAL INTEGRATIONS FRACTIONAL INTEGRATIONS, Palabras: GRASSMANNIAN MANIFOLDS GRASSMANNIAN MANIFOLDS, Palabras: INVARIANT DIFFERENTIAL OPERATORS INVARIANT DIFFERENTIAL OPERATORS, Palabras: INVERSE RADON TRANSFORM INVERSE RADON TRANSFORM, Palabras: LIE GROUPS LIE GROUPS, Palabras: SYMMETRIC DOMAINS SYMMETRIC DOMAINS

Resumen
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Let $ \mathbb{K}=\mathbb{R}, \mathbb{C}, \mathbb{H}$be the field of real, complex or quaternionic numbers and $ M_{p, q}(\mathbb{K})$the vector space of all $ p\times q$-matrices. Let $ X$be the matrix unit ball in $ M_{n-r, r}(\mathbb{K})$consisting of contractive matrices. As a symmetric space, $ X=G/K=O(n-r, r)/O(n-r)\times O(r)$, $ U(n-r, r)/U(n-r)\times U(r)$and respectively $ Sp(n-r, r)/Sp(n-r)\times Sp(r)$. The matrix unit ball $ y_0$in $ M_{r^\prime-r, r}$with $ r^\prime \le n-1$is a totally geodesic submanifold of $ X$and let $ Y$be the set of all $ G$-translations of the submanifold $ y_0$. The set $ Y$is then a manifold and an affine symmetric space. We consider the Radon transform $ \mathcal Rf(y)$for functions $ f\in C_0^\infty(X)$defined by integration of $ f$over the subset $ y$, and the dual transform $ \mathcal R^t F(x), x\in X$for functions $ F(y)$on $ Y$. For $ 2r <n, 2r\le r^\prime$with a certain evenness condition in the case $ \mathbb{K}=\mathbb{R}$, we find a $ G$-invariant differential operator $ \mathcal M$and prove it is the right inverse of $ \mathcal R^t \mathcal R$, $ \mathcal R^t \mathcal R \mathcal M f=c f$, for $ f\in C_0^\infty(X)$, $ c\ne 0$. The operator $ f\to \mathcal R^t\mathcal Rf$is an integration of $ f$against a (singular) function determined by the root systems of $ X$and $ y_0$. We study the analytic continuation of the powers of the function and we find a Bernstein-Sato type formula generalizing earlier work of the author in the set up of the Berezin transform. When $ X$is a rank one domain of hyperbolic balls in $ \mathbb{K}^{n-1}$and $ y_0$is the hyperbolic ball in $ \mathbb{K}^{r^\prime -1}$, $ 1<r^\prime<n$we obtain an inversion formula for the Radon transform, namely $ \mathcal M\mathcal R^t\mathcal R f=c f$. This generalizes earlier results of Helgason for non-compact rank one symmetric spaces for the case $ r^\prime=n-1$.

 

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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