Classification of symmetric pairs with discretely decomposable restrictions of (g,K)-modules

We give a complete classification of reductive symmetric pairs (g, h) with the following property: there exists at least one infinite-dimensional irreducible (g,K)-module X that is discretely decomposable as an (h,H \cap K)-module. We investigate further if such X can be taken to be a minimal representation, a Zuckerman derived functor module A_q(\lambda), or some other unitarizable (g,K)-module. The tensor product $\pi_1 \otimes \pi_2$ of two infinite-dimensional irreducible (g,K)-modules arises as a very special case of our setting. In this case, we prove that $\pi_1 \otimes \pi_2$ is discretely decomposable if and only if they are simultaneously highest weight modules.Comment: To appear in Crelles J. (19 pages

Classification of discretely decomposable A_q(\lambda) with respect to reductive symmetric pairs

We give a classification of the triples (g,g',q) such that Zuckerman's derived functor (g,K)-module A_q(\lambda) for a \theta-stable parabolic subalgebra q is discretely decomposable with respect to a reductive symmetric pair (g,g'). The proof is based on the criterion for discretely decomposable restrictions by the first author and on Berger's classification of reductive symmetric pairs.Comment: final version (to appear in Advances in Mathematics

A lack of classical Cepheids in the inner part of the Galactic disk

Recent large-scale infrared surveys have been revealing stellar populations in the inner Galaxy seen through strong interstellar extinction in the disk. In particular, classical Cepheids with their period-luminosity and period-age relations are useful tracers of Galactic structure and evolution. Interesting groups of Cepheids reported recently include four Cepheids in the Nuclear Stellar Disk (NSD), about 200 pc around the Galactic Centre, found by Matsunaga et al. and those spread across the inner part of the disk reported by Dekany and collaborators. We here report our discovery of nearly thirty classical Cepheids towards the bulge region, some of which are common with Dekany et al., and discuss the large impact of the reddening correction on distance estimates for these objects. Assuming that the four Cepheids in the NSD are located at the distance of the Galactic Centre and that the near-infrared extinction law, i.e. wavelength dependency of the interstellar extinction, is not systematically different between the NSD and other bulge lines-of-sight, most of the other Cepheids presented here are located significantly further than the Galactic Centre. This suggests a lack of Cepheids in the inner 2.5 kpc region of the Galactic disk except the NSD. Recent radio observations show a similar distribution of star-forming regions.Comment: 8 pages, 4 figures, accepted for publication in MNRA