Die Umkehrung des Satzes von Brauer-Berman-Witt über induzierte Charaktere endlicher Gruppen.
Die unzerlegbaren, positiv-definiten Klassenfunktionen der abzählbar unendlichen, symmetrischen Gruppe.
Dimension sugroups of metabelian groups.
Dirac monopole derived from representation theory
Direct decompositions and basic subgroups in commutative group rings
An attractive interplay between the direct decompositions and the explicit form of basic subgroups in group rings of abelian groups over a commutative unitary ring are established. In particular, as a consequence, we give a simpler confirmation of a more general version of our recent result in this aspect published in Czechoslovak Math. J. (2006).
Direct Decompositions of Finitely Generated Torsion-Free Nilpotent Groups.
Direct finiteness of group rings - a simple proof of the Kaplansky's conjecture for finite groups
Discrete series and the unipotent subgroup
Double Coset Decompositions and Computational Harmonic Analysis on Groups.
Duality in G-algebras.
Dynamics on Character Varieties and Malgrange irreducibility of Painlevé VI equation
We consider representations of the fundamental group of the four punctured sphere into . The moduli space of representations modulo conjugacy is the character variety. The Mapping Class Group of the punctured sphere acts on this space by symplectic polynomial automorphisms. This dynamical system can be interpreted as the monodromy of the Painlevé VI equation. Infinite bounded orbits are characterized: they come from -representations. We prove the absence of invariant affine structure (and invariant...
Ein Induktionssatz für rationale Charaktere von nilpotenten Gruppen.
Ein Sylowsatz für endliche p-Untergruppen von GL (n,Z).
Eine Invariante endlicher Gruppen.
Éléments réguliers et représentations de Gelfand-Graev des groupes réductifs non connexes
Soient un groupe algébrique réductif connexe défini sur et l’endomorphisme de Frobenius correspondant. Soit un automorphisme rationnel quasi-central de . Nous construisons ci-dessous l’équivalent des représentations de Gelfand-Graev du groupe , lorsque est unipotent et lorsqu’il est semi-simple. Nous montrons de plus que ces représentations vérifient des propriétés semblables à celles vérifiées par les représentations de Gelfand-Graev dans le cas connexe en particulier par rapport aux...
Endotrivial modules over groups with quaternion or semi-dihedral Sylow 2-subgroup
Let be a finite group with a Sylow 2-subgroup which is either quaternion or semi-dihedral. Let be an algebraically closed field of characteristic 2. We prove the existence of exotic endotrivial -modules, whose restrictions to are isomorphic to the direct sum of the known exotic endotrivial -modules and some projective modules. This provides a description of the group of endotrivial -modules.
Entropy of Schur–Weyl measures
Relative dimensions of isotypic components of th order tensor representations of the symmetric group on letters give a Plancherel-type measure on the space of Young diagrams with cells and at most rows. It was conjectured by G. Olshanski that dimensions of isotypic components of tensor representations of finite symmetric groups, after appropriate normalization, converge to a constant with respect to this family of Plancherel-type measures in the limit when converges to a constant. The main...
Enumerating large orbits and direct condensation.
Equivalent conditions for p-nilpotence
In the first part of this paper we prove without using the transfer or characters the equivalence of some conditions, each of which would imply p-nilpotence of a finite group G. The implication of p-nilpotence also can be deduced without the transfer or characters if the group is p-constrained. For p-constrained groups we also prove an equivalent condition so that should be p-nilpotent. We show an example that this result is not true for some non-p-constrained groups. In the second part of the...
Erratum - Espace des représentations du groupe d'un noeud classique dans un groupe de Lie