  We present the results of a stellar-population analysis of Lyman-alpha
emitting galaxies (LAES) in GOODS-N at 1.9 < z < 3.5 spectroscopically
identified by the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX). We
provide a method for connecting emission-line detections from the blind
spectroscopic survey to imaging counterparts, a crucial tool needed as HETDEX
builds a massive database of ~1 million Lyman-alpha detections. Using
photometric data spanning as many as 11 filters covering 0.4-4.5 microns from
the Hubble and Spitzer Space Telescopes, we study the objects' global
properties and explore which properties impact the strength of Lyman-alpha
emission. We measure a median stellar mass of 0.8 (^+2.9_-0.5) x 10^9 Msol and
conclude that the physical properties of HETDEX spectroscopically-selected LAEs
are comparable to LAEs selected by previous deep narrow band studies. We find
that stellar mass and star formation rate correlate strongly with the
Lyman-alpha equivalent width. We then use a known sample of z>7 LAEs to perform
a proto-study of predicting Lyman-alpha emission from galaxies in the Epoch of
Reionization, finding agreement at the 1-sigma level between prediction and
observation for the majority of strong emitters.
