P-matrices in orbit spaces and invariant theory

Abstract

In many physical problems or applications one has to study functions that are invariant under the action of a symmetry group G and this is best done in the orbit space of G if one knows the equations and inequalities defining the orbit space and its strata. It is reviewed how the P-matrix is defined in terms of an integrity basis and how it can be used to determine the equations and inequalities defining the orbit space and its strata. It is shown that the P-matrix is a useful tool of constructive invariant theory, in fact, when the integrity basis is only partially known, calculating the P-matrix elements, one is able to determine the integrity basis completely.

arXiv comment12 pages, Included in the Proceeding of the 8th Int. School of Th. Physics(SSPCM05), 31/8-7/9 2005, Myczkowce, Poland

References in corpus (2)

• Orbit spaces of reflection groups with 2, 3, and 4 basic polynomial invariants
• Geometric invariant theory approach to the determination of ground states of D-wave condensates in isotropic space

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• Is our vacuum global in a 331 model with three triplets?
• On the choice of a basis of invariant polynomials of a Finite Reflection Group. Generating Formulas for $\hat{P}$-matrices of groups of the infinite series $S_n$, $A_n$, $B_n$ and $D_n$