Some new operational representations

Default Operational Representations of Military Organizations

This report is a result of a study commissioned under the auspices of the C4ISR a Cooperative Research Program (CCRP), within the OASD(C3I) b , to attempt to identify why information integration between battlefield systems has not progressed at the rate expected. It was observed that sometimes the most fundamental issues of battle command are overlooked, especially when automation is involved. ...

The Representations and Positive Type Functions of Some Homogenous Spaces

‎For a homogeneous spaces ‎$‎G/H‎$‎, we show that the convolution on $L^1(G/H)$ is the same as convolution on $L^1(K)$, where $G$ is semidirect product of a closed subgroup $H$ and a normal subgroup $K $ of ‎$‎G‎$‎. ‎Also we prove that there exists a one to one correspondence between nondegenerat $ast$-representations of $L^1(G/H)$ and representations of ...

Representations : Some Examples

Distinction of some induced representations

Let K/F be a quadratic extension of p-adic fields, σ the nontrivial element of the Galois group of K over F , and ∆ a quasi-square-integrable representation of GL(n,K). Denoting by ∆∨ the smooth contragredient of ∆, and by ∆σ the representation ∆ ◦ σ, we show that representation ofGL(2n,K) obtained by normalized parabolic induction of the representation ∆∨⊗∆σ, is distinguished with respect to G...

Semi-linear Representations: Some Examples

By an F -semi-linear G-representation we mean an F -space V with a (k-linear) G-action such that (a v) = a v for any 2 G, v 2 V and a 2 F . This is the same as a module over the algebra F hGi := F ZZ[G] with evident action of F and the diagonal action of G. If G acts on F faithfully, then F hGi is a central k-algebra. Semi-linear G-representations nite-dimensional over F form an abelian tensor ...