  We present the results from a stellar population modeling analysis of a
sample of 162 z=4.5, and 14 z=5.7 Lyman alpha emitting galaxies (LAEs) in the
Bootes field, using deep Spitzer/IRAC data at 3.6 and 4.5 um from the Spitzer
Lyman Alpha Survey, along with Hubble Space Telescope NICMOS and WFC3 imaging
at 1.1 and 1.6 um for a subset of the LAEs. This represents one of the largest
samples of high-redshift LAEs imaged with Spitzer IRAC. We find that 30/162
(19%) of the z=4.5 LAEs and 9/14 (64%) of the z=5.7 LAEs are detected at
>3-sigma in at least one IRAC band. Individual z=4.5 IRAC-detected LAEs have a
large range of stellar mass, from 5x10^8 to 10^11 Msol. One-third of the
IRAC-detected LAEs have older stellar population ages of 100 Myr - 1 Gyr, while
the remainder have ages < 100 Myr. A stacking analysis of IRAC-undetected LAEs
shows this population to be primarily low mass (8 -- 20 x 10^8 Msol) and young
(64 - 570 Myr). We find a correlation between stellar mass and the
dust-corrected ultraviolet-based star-formation rate (SFR) similar to that at
lower redshifts, in that higher mass galaxies exhibit higher SFRs. However, the
z=4.5 LAE correlation is elevated 4-5 times in SFR compared to
continuum-selected galaxies at similar redshifts. The exception is the most
massive LAEs which have SFRs similar to galaxies at lower redshifts suggesting
that they may represent a different population of galaxies than the traditional
lower-mass LAEs, perhaps with a different mechanism promoting Lyman alpha
photon escape.
