arXiv subjects
Publications and source records attributed to Jeffrey Adams.
We consider the Chevalley involution in the context of real reductive groups. We show that if G(R) is the real points of a connected reductive group, there is an involution, unique up to conjugacy by G(R), taking any semisimple element to a conjugate of its inverse. As applications we give a condition for every irreducible representation of G(R) to be self-dual, and to the Frobenius Schur indicator for such groups.
Let G be a nonlinear double cover of the real points of a connected reductive complex algebraic group with simply laced root system. We establish a uniform character multiplicity duality theory for the category of Harish-Chandra modules for G.
One aspect of the Langlands program for linear groups is lifting of characters, which relates virtual representations on a group $G$ with those on an endoscopic group for $G$. The goal of this paper is to extend this theory to nonlinear two-fold covers of real groups in the simply laced case. Suppose $\tG$ is a two-fold cover of a real reductive group $G$. The main result is that there is an operation, denoted $\Lift_G^{\tG}$, taking a stable virtual character of $G$ to 0 or a virtual genuine character of $\tG$, and $\Lift_G^{\tG}(Θ_π)$ may be explicitly computed if $π$ is a stable sum of standard modules.
We give an algorithm for computing the irreducible admissible representations of a real reductive group with regular integral infinitesimal character. This algorithm has been implemented on a computer, as part of the Atlas of Lie Groups and Representations project.
This is an introduction to the Atlas of Lie Groups and Representations software, for computing representation and structure theory of real reductive groups. The user is led through the basic commands of the software, via numerous examples. See Algorithms for Representation Theory of Real Reductive Groups, arXiv number 0807.3093, for a more complete mathematical description of the algorithm
This article has been replaced by arXiv:0807.3093