Search results for "Mathematics::Representation Theory"
showing 10 items of 113 documents
THE AMITSUR–LEVITZKI THEOREM FOR THE ORTHOSYMPLECTIC LIE SUPERALGEBRA osp(1, 2n)
2006
http://www.worldscinet.com/jaa/05/0503/S0219498806001740.html; International audience; Based on Kostant's cohomological interpretation of the Amitsur–Levitzki theorem, we prove a super version of this theorem for the Lie superalgebras osp(1, 2n). We conjecture that no other classical Lie superalgebra can satisfy an Amitsur–Levitzki type super identity. We show several (super) identities for the standard super polynomials. Finally, a combinatorial conjecture on the standard skew supersymmetric polynomials is stated.
On a question of C. Bonnafé on characters and multiplicity free constituents
2019
Abstract In 2006, C. Bonnafe posed a general question on characters of finite groups. A positive answer would have reduced drastically some proofs by G. Lusztig.
Finite Groups with Odd Sylow Normalizers
2016
We determine the non-abelian composition factors of the finite groups with Sylow normalizers of odd order. As a consequence, among others, we prove the McKay conjecture and the Alperin weight conjecture for these groups.
Irreducible induction and nilpotent subgroups in finite groups
2019
Suppose that $G$ is a finite group and $H$ is a nilpotent subgroup of $G$. If a character of $H$ induces an irreducible character of $G$, then the generalized Fitting subgroup of $G$ is nilpotent.
Brauer characters with cyclotomic field of values
2008
It has been shown in an earlier paper [G. Navarro, Pham Huu Tiep, Rational Brauer characters, Math. Ann. 335 (2006) 675–686] that, for any odd prime p, every finite group of even order has a non-trivial rational-valued irreducible p-Brauer character. For p=2 this statement is no longer true. In this paper we determine the possible non-abelian composition factors of finite groups without non-trivial rational-valued irreducible 2-Brauer characters. We also prove that, if p≠q are primes, then any finite group of order divisible by q has a non-trivial irreducible p-Brauer character with values in the cyclotomic field Q(exp(2πi/q)).
Weyl's Theorems and Extensions of Bounded Linear Operators
2012
A bounded operator $T\in L(X)$, $X$ a Banach space, is said to satisfy Weyl's theorem if the set of all spectral points that do not belong to the Weyl spectrum coincides with the set of all isolated points of the spectrum which are eigenvalues and having finite multiplicity. In this article we give sufficient conditions for which Weyl's theorem for an extension $\overline T$ of $T$ (respectively, for $T$) entails that Weyl's theorem holds for $T$ (respectively, for $\overline T$).
Fixpunktmengen von halbeinfachen Automorphismen in halbeinfachen Lie-Algebren
1976
Let g be a semisimple Lie algebra over an algebraically closed field of characteristic 0. The set of fixed points of a semisimple inner automorphism of g is a regular reductive subalgebra of maximal rank [1], so it is defined by a subsystem of the root system Φ of g relative to a suitable Cartan subalgebra. The main theorem of the article characterizes the corresponding subsystems of Φ. The second part of the article shows how to compute the fixed point algebras of semisimple outer automorphisms of g. A complete list of all fixed point algebras is then easily obtainable. The results are applied to bounded symmetric domains. References
On Higgs bundles over Shimura varieties of ball quotient type
2016
We prove the generic exclusion of certain Shimura varieties of unitary and orthogonal types from the Torelli locus. The proof relies on a slope inequality on surface fibration due to G. Xiao, and the main result implies that certain Shimura varieties only meet the Torelli locus in dimension zero.
The horospherical Gauss-Bonnet type theorem in hyperbolic space
2006
We introduce the notion horospherical curvatures of hypersurfaces in hyperbolic space and show that totally umbilic hypersurfaces with vanishing cur- vatures are only horospheres. We also show that the Gauss-Bonnet type theorem holds for the horospherical Gauss-Kronecker curvature of a closed orientable even dimensional hypersurface in hyperbolic space. + (i1) by using the model in Minkowski space. We introduced the notion of hyperbolic Gauss indicatrices slightly modified the definition of hyperbolic Gauss maps. The notion of hyperbolic indicatrices is independent of the choice of the model of hyperbolic space. Using the hyperbolic Gauss indicatrix, we defined the principal hyperbolic curv…
Unbounded C$^*$-seminorms and $*$-Representations of Partial *-Algebras
2009
The main purpose of this paper is to construct *-representations from unbounded C*-seminorms on partial *-algebras and to investigate their *-representations. © Heldermann Verlag.