V1082-Sgr: A magnetic cataclysmic variable with a lobe-filling companion star

V1082 Sgr is a cataclysmic variable with accretion luminosity above $10^{34}$erg s$^{-1}$, indicating a mass transfer rate above $10^{-9}M_{\odot}$yr$^{-1}$. However, its K type companion was suggested to be under-filling its Roche lobe (RL), making the high mass transfer rate a mystery. In this work we propose a possible model to explain this discrepancy. The system is proposed to be an intermediate polar, with its K type companion filling its RL. The mass of the white dwarf star is evaluated to be $0.77\pm0.11M_{\odot}$ from both X-ray continuum fitting and Fe line flux ratio measurements. We make numerical simulations to search for the possible progenitors of the system. The results show that a binary with an initial 1.5--2.5$M_{\odot}$ companion in a 1--2 day orbit (or an initial 1.0--1.4$M_{\odot}$ companion in a 3.2--4.1 day orbit) may naturally evolve to a cataclysmic variable with a $\sim 0.55 \pm 0.11M_{\odot}$, Roche-lobe filling companion in a 0.86 day orbit. The effective temperature of the donor star, the mass transfer rate, and the derived V band magnitude are all consistent with previous observations.