Timeline for Which metrics on exterior power are induced from metrics on the base?

6 events

when toggle format	what		by	license	comment
Jan 11, 2018 at 10:50	comment	added	Asaf Shachar		Thanks. This was also my natural guess, but that doesn't seem to be well-defined (consider what happens when you switch $v_1^,v_2^$). In fact, there is a possibility that there is no injection at all: see here.
Jan 11, 2018 at 9:54	comment	added	Peter Michor		Link corrected. I did not work out the injection. The most natural one is: $(v_1^\wedge\dots\wedge v_k^)\otimes (w_1^\wedge \dots\wedge w_k^) \mapsto \pm (v_1^\otimes w_1^)\wedge \dots \wedge (v_k^\otimes w_k^)$. One should look at the corresponding Young tableaus and identify the irreducible components as $GL(V)$-representations.
Jan 11, 2018 at 9:45	history	edited	Peter Michor	CC BY-SA 3.0	added 4 characters in body
Jan 11, 2018 at 8:08	comment	added	Asaf Shachar		Sorry, one more question: In my formulation $g:V \to V^$, and $\Lambda^kg:\Lambda^{k} V \to \Lambda^{k} (V^) \cong (\Lambda^{k} V)^$ is the induced map on exterior powers, that is an element of $\Lambda^{k} V^ \otimes \Lambda^{k} V^$. You seem to consider it as an element in $\Lambda^{k}(V^ \otimes V^)$. Can you please say how exactly do you identify $\Lambda^{k} V^ \otimes \Lambda^{k} V^$ as a subset of $\Lambda^{k}(V^ \otimes V^*)$? Thanks.
Jan 11, 2018 at 7:39	comment	added	Asaf Shachar		Thanks, though I think the link you provided doesn't work (at least for me).
Jan 11, 2018 at 7:28	history	answered	Peter Michor	CC BY-SA 3.0