Invariants and relative invariants under compact Lie groups

Isometric Actions of Lie Groups and Invariants

This are the notes of a lecture course held by P. Michor at the University of Vienna in the academic year 1992/1993, written by Konstanze Rietsch. The lecture course was held again in the academic year 1996/97 and the notes were corrected and enlarged by P. Michor.

Differential Invariants for Lie Pseudo-groups

Lie pseudo-groups, roughly speaking, are the infinite-dimensional counterparts of local Lie groups of transformations. Pseudo-groups were first studied systematically at the end of the 19th century by Sophus Lie, whose great insight in the subject was to postulate the additional condition that pseudo-group transformations form the general solution to a system of partial differential equations, ...

Asymptotics of Matrix Integrals and Tensor Invariants of Compact Lie Groups

Abstract. In this paper we give an asymptotic formula for a matrix integral which plays a crucial role in the approach of Diaconis et al. to random matrix eigenvalues. The choice of parameter for the asymptotic analysis is motivated by an invariant theoretic interpretation of this type of integral. For arbitrary regular irreducible representations of arbitrary connected semisimple compact Lie g...

Moving Frames and Differential Invariants for Lie Pseudo-groups

We survey a recent extension of the moving frames method for infinite-dimensional Lie pseudo-groups. Applications include a new, direct approach to the construction of Maurer–Cartan forms and their structure equations for pseudogroups, and new algorithms, based on constructive commutative algebra, for uncovering the structure of the algebra of differential invariants for pseudogroup actions.

University of Cambridge Lie Groups and the Computation of Invariants