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This article studies components of Springer fibers for $𝔤𝔩 (n)$ that are associated to closed orbits of $G L (p) \times G L (q)$ on the flag variety of $G L (n), n = p + q$ . These components occur in any Springer fiber. In contrast to the case of arbitrary components, these components are smooth varieties. Using results of Barchini and Zierau we show these components are iterated bundles and are stable under the action of a maximal torus of $G L (n)$ . We prove that if $ℒ$ is a line bundle on the flag variety associated to a dominant weight, then the higher...

Smoothness and analycity for solutions of first order systems of partial differential equations on nilpotent Lie groups.

Lawrence. Corwin, B. Helffer (1985)

Inventiones mathematicae

Smoothness of densities of semigroups of measures on homogeneous groups

Jacek Dziubański, Jacek Zienkiewicz (1993)

Colloquium Mathematicae

Some applications of seesaw duality to branching laws.

Dipendra Prasad (1996)

Mathematische Annalen

Some basic properties of theta series. (Quelques propriétés de base de séries théta.)

Mœglin, Colette (1997)

Journal of Lie Theory

Some geometrical properties of infinite-dimensional bilinear controlled systems

Naceurdine Bensalem, Fernand Pelletier (1999)

Banach Center Publications

The study of controlled infinite-dimensional systems gives rise to many papers (see for instance [GXL], [GXB], [X]) but it is also motivated by various mathematical problems: partial differential equations ([BP]), sub-Riemannian geometry on infinite-dimensional manifolds ([Gr]), deformations in loop-spaces ([AP], [PS]). The first difference between finite and infinite-dimensional cases is that solutions in general do not exist (even locally) for every given control function. The aim of this paper...

Some groups whose reduced $C^{*}$ -algebra is simple

M. Bekka, M. Cowling, P. de La Harpe (1994)

Publications Mathématiques de l'IHÉS

Some Hardy type inequalities in the Heisenberg group.

Han, Yazhou, Niu, Pengcheng (2003)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Some linear groups virtually having a free quotient.

Margulis, G.A., Vinberg, È.B. (2000)

Journal of Lie Theory

Some nonzero cohomology of discrete groups.

Y.L. Tong, S.P. Wang (1987)

Journal für die reine und angewandte Mathematik

Some oscillatory integrals and their applications

E. M. Stein (1984/1985)

Séminaire Équations aux dérivées partielles (Polytechnique)

Some properties of Carnot-Carathéodory balls in the Heisenberg group

Roberto Monti (2000)

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

Using the exact representation of Carnot-Carathéodory balls in the Heisenberg group, we prove that: 1. $|\nabla_{H^{n}} d (z, t)| = 1$ in the classical sense for all $(z, t) \in H^{n}$ with $z \neq 0$ , where $d$ is the distance from the origin; 2. Metric balls are not optimal isoperimetric sets in the Heisenberg group.

Some relations among volume, intrinsic perimeter and one-dimensional restrictions of $B V$ functions in Carnot groups

Francescopaolo Montefalcone (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let $𝔾$ be a $k$ -step Carnot group. The first aim of this paper is to show an interplay between volume and $𝔾$ -perimeter, using one-dimensional horizontal slicing. What we prove is a kind of Fubini theorem for $𝔾$ -regular submanifolds of codimension one. We then give some applications of this result: slicing of $B V_{𝔾}$ functions, integral geometric formulae for volume and $𝔾$ -perimeter and, making use of a suitable notion of convexity, called $𝔾$ -convexity, we state a Cauchy type formula for $𝔾$ -convex sets. Finally,...

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SL2-triplet associé à un polynôme homogène.

Small solutions to linear congruences and Hecke equidistribution

Smooth and admissible representations of $p$ -adic unipotent groups

Smooth classification of Cartan actions of higher rank semisimple Lie groups and their lattices.

Smooth components of Springer fibers