Abstract. We relate poles of local Godement-Jacquet L-functions to distributions on matrix spaces with singular supports. As an application, we show the irreducibility of the full theta lifts to GL n (F) of generic irreducible representations of GL n (F), where F is an arbitrary local field.
Let G be a connected compact Lie group. Among other things, we prove that the following are equivalent. (a) For all connected compact Lie groups H and all continuous homomorphisms φ, φ : H → G, if φ(h) and φ (h) are conjugate in G for all h ∈ H, then φ and φ are G-conjugate. (b) The Lie algebra of G contains no simple ideal of type D n (n ≥ 4), E 6 , E 7 , or E 8 .
An improved stream cipher based on the linear feedback shift register is set up by adding disturbance on to the initial states. The key advantage of the new algorithm over the already proposed ones is that the characters of the ciphertext corresponding to the same characters in the plaintext are distinct. The new algorithm also keeps all other advantages. Therefore, for the adversary, it is more difficult to make an attack by analyzing the statistics data of the characters.
In this article we provide two kinds of infinite presentations of toroidal Lie algebras. At first we define generalized Heisenberg algebras and prove that each toroidal Lie algebra is an amalgamation of a simple Lie algebra and a generalized Heisenberg algebra in the sense of Saito and Yoshii. This is one kind of presentations of toroidal Lie algebras given by the generators of generalized Heisenberg algebras and the Chevalley generators of simple Lie algebras with certain amalgamation relations. Secondly by using the generalized Chevalley generators, we give another kind of presentations. These two kinds of presentations are different from those given by Moody, Eswara Rao and Yokonuma.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.