Timeline for Representation Theory of $U(N)$

9 events

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Jun 21, 2015 at 23:00	comment	added	André Henriques		There are two possible ways of interpreting the sentence "it cannot respect the tensor product structure". It matters whether or not not includes the symmetry isomorphisms. Have a look at the first 3 paragraphs of the intro of arxiv.org/pdf/math/0007196.pdf for a relevant discussion.
Jun 20, 2015 at 22:05	comment	added	André Henriques		The sentence "respect the tensor product structure and the duality of representations" is equivalent to "respect the tensor product structure". There is no such thing as "respecting the duality". Or, in other words, "respecting the duality" is a formal consequence of "respecting the tensor product structure".
Jun 20, 2015 at 21:45	answer	added	andrewBee		timeline score: 1
Jun 20, 2015 at 20:51	review	Close votes
Jun 21, 2015 at 6:47
Jun 20, 2015 at 17:56	history	edited	Andrea Pena	CC BY-SA 3.0	added 6 characters in body
Jun 20, 2015 at 17:26	review	Suggested edits
Jun 20, 2015 at 17:42
Jun 20, 2015 at 16:39	answer	added	Sam Gunningham		timeline score: 6
Jun 20, 2015 at 15:03	comment	added	asv		Even if such an equivalence of categories exists, it cannot respect the tensor product structure and the duality of representations. Otherwise the Tannaka-Krein theorem would imply an isomorphism of groups $U(n)$ and $SU(n)\times U(1)$, which are not isomorphic.
Jun 20, 2015 at 14:47	history	asked	Andrea Pena	CC BY-SA 3.0