We present a study of stellar populations in a sample of spectroscopically-confirmed Lyman-break galaxies (LBGs) and Ly$alpha$ emitters (LAEs) at $5.7<z<7$. These galaxies have deep optical and infrared images from Subaru, $HST$, and $Spitzer$/IRAC. We focus on a subset of 27 galaxies with IRAC detections, and characterize their stellar populations utilizing galaxy synthesis models based on the multi-band data and secure redshifts. By incorporating nebular emission estimated from the observed Ly$alpha$ flux, we are able to break the strong degeneracy of model spectra between young galaxies with prominent nebular emission and older galaxies with strong Balmer breaks. The results show that our galaxies cover a wide range of ages from several to a few hundred million years (Myr), and a wide range of stellar masses from $sim10^8$ to $sim10^{11}$ $M_{odot}$. These galaxies can be roughly divided into an `old subsample and a `young subsample. The `old subsample consists of galaxies older than 100 Myr, with stellar masses higher than $10^9$ $M_{odot}$. The galaxies in the `young subsample are younger than $sim$30 Myr, with masses ranging between $sim10^8$ and $sim3times10^9$ $M_{odot}$. Both subsamples display a correlation between stellar mass and star-formation rate (SFR), but with very different normalizations. The average specific SFR (sSFR) of the `old subsample is 3--4 Gyr$^{-1}$, consistent with previous studies of `normal star-forming galaxies at $zge6$. The average sSFR of the `young subsample is an order of magnitude higher, likely due to starburst activity. Our results also indicate little or no dust extinction in the majority of the galaxies, as already suggested by their steep rest-frame UV slopes. Finally, LAEs and LBGs with strong Ly$alpha$ emission are indistinguishable in terms of age, stellar mass, and SFR.
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