2014/10/30 by I. Penkov, Penkov, I., A. Petukhov +1
Mathematics · #16G #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:16G
paper · pdf · doi:10.48550/arxiv.1410.8430
arxiv created 2014/10/30 · arxiv updated 2014/10/31
We give a criterion for the annihilator in U(\fraksl(∞)) of a simple highest weight \fraksl(∞)-module to be nonzero. As a consequence we show that, in contrast with the case of \fraksl(n), the annihilator in U(\fraksl(∞)) of any simple highest weight \fraksl(∞)-module is integrable, i.e., coincides with the annihilator of an integrable \fraksl(∞)-module. Furthermore, we define the class of ideal Borel subalgebras of \fraksl(∞), and prove that any prime integrable ideal in U(\fraksl(∞)) is the annihilator of a simple \frak b0-highest weight module, where \frak b0 is any fixed ideal Borel subalgebra of \fraksl(∞). This latter result is an analogue of the celebrated Duflo Theorem for primitive ideals.