Joël Merker (Paris-Saclay U.): Differential Invariants, Recurrence Relations, and Homogeneous Models
Channel: Centrum Fizyki Teoretycznej PAN
Date: 2021-09-15

Joël Merker (Paris-Saclay U.)
Differential Invariants, Recurrence Relations, and Homogeneous Models.
Finite or infinite-dimensional group actions on submanifolds produce large collections of differential invariants. Explicit expressions rapidly become unwieldy. Fortunately, the Fels-Olver recurrence relations enable to reach the heart of the matter, without having to handle huge formulas. Naturally, branches and subbranches created by (relative) differential invariants carry their own recurrence relations. The Janet-Riquier theory then becomes concrete, motivated by geometric problems and various group actions. An alternative view can be developed by means of power series expansions at only one point, say the origin. This, again, lowers the computational complexity. In particular, the production of all homogeneous models of a given geometric structure can be reduced to linear algebra computations. Also, Cartan’s method of equivalence can be enhanced accordingly.

GRIEG collaboration project: SCREAM workshop 2021.