Book Review: Classical invariant theory

Transcending Classical Invariant Theory

Let SP2n(R) = SP2n = Sp be the real symplectic group of rank n. Let Sp denote the two-fold cover of Sp. There is a unitary representation, constructed by Shale [Sh] and Weil [WA], of Sp that is of considerable interest in the theory of automorphic forms. We denote this representation by wand call it the oscillator representation. The purpose of this paper is to establish about w a fact that sho...

Remarks on Classical Invariant Theory

A uniform formulation, applying to all classical groups simultaneously, of the First Fundamental Theory of Classical Invariant Theory is given in terms of the Weyl algebra. The formulation also allows skew-symmetric as well as symmetric variables. Examples illustrate the scope of this formulation.

Graph Theory and Classical Invariant Theory

Classical invariant theory has died and been resurrected many times. Its golden age in the last century was marked with the flowering of unsurpassed computational ability, and the explicit determination of the invariants of most of the elementary polynomials. The computational approach is commonly acknowledged to have been dealt a death-blow by Hilbert’s celebrated Basis Theorem, an existential...

Book Review: Contemporary Sensorimotor Theory

Consciousness, with its irreducible subjective character, was almost exclusively a philosophical topic until relatively recently. Today, however, the problem of explaining the felt quality of experience has also become relevant to science and engineering, including robotics andAI: “What would we have to build into a robot so that it really felt the touch of a finger, the redness of red, or the ...

Standard Monomial Theory for Harmonics in Classical Invariant Theory