❓ [QUESTION] About parity in irreducible representation

[hyuntae-cho]

For O(3) representation, parity variable is adopted which represents reflections.
From what I've understand, when we apply (x,y,z) |-> (-x,-y,-z) action to all coordinates, every parity of feature representations should change.
However, it seems nequip.nn.embedding.SphericalHarmonicEdgeAttrs always calculate edge attribute with fixed irreducible representations.
Could you explain more about it? Thanks for your time! :)

[Linux-cpp-lisp]

Hi @choant ,

This is almost correct--- the key is that the parity in the irrep does not describe the sign of the data itself, but rather how that sign should transform under inversions. The L=1 spherical harmonic, for example, is a vector and thus has odd parity (-1); this means that when you invert the input coordinates the sign of the L=1 tensor flips. What parity -1 in the irrep signifies is that this flip occurs, not the current "state" of the sign for some particular data that transforms according to the irrep.