I know that usually, the way to compare the Hilbert spaces arising from $SU(2)$ ChernSimons theory with different Kähler polarizations is via the Hitchin connection. However, it should be possible, I would think, to try to use a BKS pairing between them. Are any results known on whether this pairing is unitary? (My guess would be that the answer is no, based upon the results of Kirwin et al for toric varieties, but then the character varieties that are quantized in ChernSimons theory aren't really toric varieties).
Likewise for real polarizations, I know Jeffrey and Weitsman did some work on BKS pairings but I don't recall seeing any theorems in their papers about whether the pairing was unitary for real polarizations in general. Has there been further work done on the pairings for real polarizations?
Take the 2minute tour
×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.


