These are from House 2 at Ephesus and may represent a lintel or part of piece of furniture.
The emperor is clearly Trajan and while the museum labeling and catalogue entry leaves open what campaign it celebrates (Dacian or Parthian), I’m pretty certain this is Dacian. If you search ivory and Ephesus on Flickr there are some other pictures by other people, many with better images than mine, but I wanted a set of all the details for myself. I’m particularly interested in the lower relief which shows a scene that is not military. It gets no real discussion in the catalogue. (Do you know where it has been published? Let me know! My copy of the book published on these houses is back in the US, so I’ve not checked there yet.)
More on this scene after the gallery of images. My initial interpretation is that one panel shows offerings to the gods and the other a more bureaucratic scene perhaps of tribute being inventoried.
Figure 1 stands perhaps with an object(s) in his hand (f), perhaps a tray of offerings for figure 2? His attitude, however, is also reminiscent of Hermes/Mercury in some representations. Figure 2 seems to hold a small statue (e) similar to how the palladium is typically represented (side view of archaic figure with round shield spear and helmet). The bare legs rule out Athena/Minerva, but perhaps a personification of Roma or similar? The bench on which figures 5 and 4 sit could accommodate another seated figure (3), whose may rest on a small stool (d) whols legs are just visible. Notice Figure 5 and 4 are in conversation. 4 have longer drapery than 5. They are being made an offering of some sort (c).
Figures 11, 10 and 9 all process towards Figure 8. Figure 8 is heavily draped and may be in 3/4 or full frontal view. Figure 9 may wear trousers and some sort of sash is visible between his legs; his offer ins completely lost. Figure 10 holds up Object b in a manner suggesting it may be lightweight. The drapery of figure 10 is so complete it obscures feet and may cover head. Figure 11 is draped in a different manner and holds a narrow cloth object that drapes over the hand; their arm is held closer to their body. Figure 8 seems likely to be a female deity. I’m not confident about the genders of figures 11 and 10.
Figure 8 and Figure 5 are included here for visual reference. Figure seven is less heavily draped and has ankles and calf visible, hair is chin length, likely male, and approaches a set of doors (of a sanctuary?). On the opposite side of the door is figure 6 with slightly shorter garments (calves visible) approaches and offers object c.
Figure 1 and nearby objects are included for reference. It is not clear to me that this panel was ever actually attached to the preceding one. Notice the distinct break to the right of the door. Perhaps find data influenced this juxtaposition in the display. Figure 12 seems to wear a toga and gesture with right arm towards a large door. His right food seems to be raised perhaps on step before the door? Over his arm is perhaps a case of some sort (l). I’m not certain what is like to have been between Figures 12 and 13. Figure 13 presents a box (k) to the two seated figures (14 and 15). At his feet is a cylindrical case, likely a scroll box (j). Figure 13’s drapery is not as obviously a toga as it covers feet, but perhaps it is a toga after all. The seated figures (14 and 15) seem to be officials or magistrates on a subsellium.
Figure 15 is included for reference. Figure 16 is dressed in a workman’s tunic and bends over to offer a heavy round object (i) to Figure 15 (and 14?). The round object could be a shield, but is perhaps better interpreted as a precious metal plate (e.g. a lanx). Object h appears to be a strong-box shown in partial perspective. The mark on the short end appears to be a keyhole/lock. Figure 17 reaches towards the box and is likely togate.
Figure 17 is include for reference. Object(s) g on the table maybe similar to object i but seen from the side. I think precious metal plate is most likely. The table like the strong-box is shown in poorly rendered 3D. Figure 18 stands behind the the table as is likely to also be wearing a toga. Figures 19-22 descend a ramp or staircase made of ashlar masonry and constructed out of arches. They maybe entering the work area (carrying materials?) in which the other figures are occupied.