Results 11 to 20 of about 16,949 (276)
Restrictions of generalized Verma modules to symmetric pairs [PDF]
Transformation Groups 17 (2012), pp. 523-546, 2010 We initiate a new line of investigation on branching problems for generalized Verma modules with respect to complex reductive symmetric pairs (g,k). Here we note that Verma modules of g may not contain any simple module when restricted to a reductive subalgebra k in general.
C Benson +10 more
arxiv +3 more sources
Regions in the dominant chamber and nilpotent orbits [PDF]
Bull. Sci. Math. 128 (2004), 1-6, 2003 We give a geometric description for the dominant characteristic of a nilpotent orbit in an arbitrary finite-dimensional rational G-module. In particular, we obtain a generalization of a recent result of Gunnells-Sommers, see math.RT/0212089.
Panyushev, Dmitri I.
arxiv +4 more sources
G -complete reducibility and semisimple modules [PDF]
, 2011 Let $G$ be a connected reductive algebraic group defined over an algebraically closed field %$k$ of characteristic $p > 0$. Our first aim in this note is to give concise and uniform proofs for two fundamental and deep results in the context of Serre's ...
Michael Bate +3 more
openalex +3 more sources
The exterior algebra and ?spin? of an orthogonal $$\mathfrak{g}$$ -module
Transformation Groups, 2001 A well-known result of Kostant gives a description of the G-module structure for the exterior algebra of Lie algebra $\frak g$. We give a generalization of this result for the isotropy representations of symmetric spaces. If $\frak g={\frak g}_0+{\frak g_1}$ is a Z_2-grading of a simple Lie algebra, we explicitly describe a ${\frak g}_0$-module $Spin_0(
Dmitri I. Panyushev
openaire +5 more sources
MPC Protocol for G-module and its Application in Secure Compare and ReLU [PDF]
arXiv, 2020 Secure comparison and secure selection are two fundamental MPC (secure Multi-Party Computation) protocols. One important application of these protocols is the secure ReLU and DReLU computation in privacy preserving deep learning. In this paper, we introduce G-module, a mathematics tool, to re-design such protocols.
Qizhi Zhang +3 more
arxiv +2 more sources
Cohomologies of finite abelian groups [PDF]
Algebra Discrete Math. 24, no.1 (2017) 144-157, 2017 We construct a simplified resolution for the trivial G-module Z, where G is a finite abelian group, and compare it with the standard resolution. We use it to calculate cohomologies of irreducible G-lattices and their duals.
Drozd, Yuriy A., Plakosh, Andriana I.
arxiv +4 more sources
The third cohomology group classifies crossed module extensions [PDF]
arXiv, 2009 We give an elementary proof of the well-known fact that the third cohomology group H^3(G, M) of a group G with coefficients in an abelian G-module M is in bijection to the set Ext^2(G, M) of equivalence classes of crossed module extensions of G with M.
Thomas, Sebastian
arxiv +2 more sources
Group extensions with special properties [PDF]
arXiv, 2014 Given a group G and a G-module A, we show how to determine up to isomorphism the extensions E of A by G so that A embeds as smallest non-trivial term of the derived series or of the lower central series into E.
Distler, Andreas, Eick, Bettina
arxiv +3 more sources
An algorithm to compute the canonical basis of an irreducible Uq(g)-module
LMS Journal of Computation and Mathematics, 2002 An algorithm is described to compute the canonical basis of an irreducible module over a quantized enveloping algebra of a finite-dimensional semisimple Lie algebra. The algorithm works for modules that are constructed as a submodule of a tensor product of modules with known canonical bases.
Willem A. de Graaf
openaire +5 more sources
On transfer in bounded cohomology [PDF]
arXiv, 2009 We define a transfer map in the setting of bounded cohomology with certain metric G-module coefficients. As an application, we extend a theorem of Chatterji, Mislin, Pittet and Saloff-Coste on the comparison map from Borel-bounded to Borel cohomology, to cover the case of Lie groups with finitely many connected components.
Chatterji, Indira, Mislin, Guido
arxiv +2 more sources