Monoid Embeddings of Symmetric Varieties
  We determine when an antiinvolution on an adjoint semisimple linear algebraic group extends to an antiinvolution on a $J$-irreducible monoid. Using this information, we study a special class of compactifications of symmetric varieties. Extending the work of Springer on involutions, we describe the parametrizing sets of Borel orbits in these special embeddings. 
Mahir Bilen Can and Roger Howe and Lex Renner
math.AG math.RT