Classical Invariant Theory for the Quantum Symplectic Group

Quantum Group Gauge Theory on Classical Spaces

We study the quantum group gauge theory developed elsewhere in the limit when the base space (spacetime) is a classical space rather than a general quantum space. We show that this limit of the theory for gauge quantum group Uq(g) is isomorphic to usual gauge theory with Lie algebra g. Thus a new kind of gauge theory is not obtained in this way, although we do find some differences in the coupl...

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...

Standard Monomial Theory for Harmonics in Classical Invariant Theory