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Geometric control theory and Riemannian techniques are used to describe the reachable set at time t of left invariant single-input control systems on semi-simple compact Lie groups and to estimate the minimal time needed to reach any point from identity. This method provides an effective way to give an upper and a lower bound for the minimal time needed to transfer a controlled quantum system with a drift from a given initial position to a given final position. The bounds include diameters...

An example of Fourier transforms of orbital integrals and their endoscopic transfer.

Everling, Ulrich (1998)

The New York Journal of Mathematics [electronic only]

An example of unipotent representations associated with a nilpotent nonminimal orbit: The case of orbits of dimension 10 of $s o (4, 3)$ . (Un exemple de représentations unipotentes associées à une orbite nilpotente non minimale: le cas des orbites de dimension 10 de $s o (4, 3)$ .)

Sabourin, Hervé (2000)

Journal of Lie Theory

An explicit computation of $p$ -stabilized vectors

Michitaka MIYAUCHI, Takuya YAMAUCHI (2014)

Journal de Théorie des Nombres de Bordeaux

In this paper, we give a concrete method to compute $p$ -stabilized vectors in the space of parahori-fixed vectors for connected reductive groups over $p$ -adic fields. An application to the global setting is also discussed. In particular, we give an explicit $p$ -stabilized form of a Saito-Kurokawa lift.

An explicit construction of the K-finite vectors in the discrete series for an isotropic semisimple symmetric space

Mogens Flensted-Jensen, Kiyosato Okamoto (1984)

Mémoires de la Société Mathématique de France

An explicit construction of the metaplectic representation over a finite field.

Neuhauser, Markus (2002)

Journal of Lie Theory

An extension of Mahler's theorem to simply connected nilpotent groups

Martin Moskowitz (2005)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

This Note gives an extension of Mahler's theorem on lattices in $R^{n}$ to simply connected nilpotent groups with a $Q$ -structure. From this one gets an application to groups of Heisenberg type and a generalization of Hermite's inequality.

An extension of the Khinchin-Groshev theorem

Anish Ghosh, Robert Royals (2015)

Acta Arithmetica

We prove a version of the Khinchin-Groshev theorem in Diophantine approximation for quadratic extensions of function fields in positive characteristic.

An extention of Nomizu’s Theorem –A user’s guide–

Hisashi Kasuya (2016)

Complex Manifolds

For a simply connected solvable Lie group G with a lattice Γ, the author constructed an explicit finite-dimensional differential graded algebra A*Γ which computes the complex valued de Rham cohomology H*(Γ, C) of the solvmanifold Γ. In this note, we give a quick introduction to the construction of such A*Γ including a simple proof of H*(A*Γ) ≅ H*(Γ, C).

An F. and M. Riesz theorem for compact Lie groups.

R.G.M. Brummelhuis (1989)

Mathematica Scandinavica

An inequality for local unitary Theta correspondence

Z. Gong, L. Grenié (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

Given a representation $π$ of a local unitary group $G$ and another local unitary group $H$ , either the Theta correspondence provides a representation $θ_{H} (π)$ of $H$ or we set $θ_{H} (π) = 0$ . If $G$ is fixed and $H$ varies in a Witt tower, a natural question is: for which $H$ is $θ_{H} (π) \neq 0$ ? For given dimension $m$ there are exactly two isometry classes of unitary spaces that we denote $H_{m}^{\pm}$ . For $ε \in {0, 1}$ let us denote $m_{ε}^{\pm} (π)$ the minimal $m$ of the same parity of $ε$ such that $θ_{H_{m}^{\pm}} (π) \neq 0$ , then we prove that $m_{ε}^{+} (π) + m_{ε}^{-} (π) \geq 2 n + 2$ where $n$ is the dimension of $π$ .

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Displaying 181 – 200 of 260

An analogue of the Weil representation for G2.

An application of the building to orbital integrals

An elementary approach to the hypergeometric shift operators of Opdam.

An Elementary Proof of the Baker-Campbell-Hausdorff-Dynkin Formula.

An endpoint estimate for the Kunze-Stein phenomenon and related maximal operators.

An estimation of the controllability time for single-input systems on compact Lie Groups