We present combinatorial operators for the expansion of the Kronecker product of irreducible representations of the symmetric group Sn. These combinatorial operators are defined in the ring of symmetric functions and act on the Schur functions basis. This leads to a combinatorial description of the Kronecker powers of the irreducible representations indexed with the partition (n− 1, 1) which sp...

Let Sn denote the full symmetric permutation group of degree n. For each a E e, let (J (a) be the corresponding permutation matrix, i.e., Q(a) = (0 iUU»)' If e is any subgroup of S n, then Q is a faithful representation of e whose c haracter, e, counts the number of fixed points . In trus note, we in vestigate a red uction of fr, the character of the rth Kronecker power of (J . The reduction of...

In this paper we introduce two symmetric variants of amenability, symmetric module amenability and symmetric Connes amenability. We determine symmetric module amenability and symmetric Connes amenability of some concrete Banach algebras. Indeed, it is shown that $ell^1(S)$ is  a symmetric $ell^1(E)$-module amenable if and only if $S$ is amenable, where $S$ is an inverse semigroup with subsemigr...

High-power microwave amplifier operation has been studied for use in a number of applications. The performance of the amplifiers has been marred, in some cases, by pulse shortening of the microwave signal. A possible source of the shortening is the loss of the beam due to hybrid HEM11 mode interaction with the beam. In this paper, we describe experiments which investigate high-power operation a...

Addressing the need for passive magneto-inductive components, a lumped-element symmetric power divider has been designed and realised for a magneto-inductive cable with the resonant frequency of 95 MHz and the passband between 73 and 174 MHz. In agreement with the theory, the measured coupling loss is 6 dB for most of the passband independent of the input port. Having proved useful for magneto-...

82 IEEE Concurrency R symmetric multiprocessor systems have become widely available, both as computational servers and as platforms for high-performance parallel computing. The same trend is found in PCs—some have also become SMPs with many CPUs in one box. Clusters of PC-based SMPs are expected to be compact, cost-effective parallel-computing platforms. At the Real World Computing Partnership,...

We describe some of the determinantal ideals attached to symmetric, exterior and tensor powers of a matrix. The methods employed use elements of Zariski’s theory of complete ideals and of representation theory. Let R be a commutative ring. The determinantal ideals attached to matrices with entries in R play ubiquitous roles in the study of the syzygies of R–modules. In this note, we describe so...

The conjectures of Deligne, Bĕılinson, and Bloch-Kato assert that there should be relations between the arithmetic of algebrogeometric objects and the special values of their L-functions. We make a numerical study for symmetric power L-functions of elliptic curves, obtaining data about the validity of their functional equations, frequency of vanishing of central values, and divisibility of Bloc...

For each positive integer k, using techniques of Dwork’s, we investigate the L-function defined by the k-th symmetric power of the F -crystal associated to the family of exponential sums of x + λx where λ runs over F ∗ p. In particular, we will explore its rationality, coefficients, degree, trivial factors, functional equation, and Newton polygon.

The conjectures of Deligne, Bĕılinson, and Bloch-Kato assert that there should be relations between the arithmetic of algebrogeometric objects and the special values of their L-functions. We make a numerical study for symmetric power L-functions of elliptic curves, obtaining data about the validity of their functional equations, frequency of vanishing of central values, and divisibility of Bloc...