  Ian Grojnowski has developed a purely algebraic way to connect the
representation theory of affine Hecke algebras at an (l+1)-th root of unity to
the highest weight theory of the affine Kac-Moody algebra of type A_l^(1). The
present article is devoted to extending Grojnowski's machinery to the twisted
case: we replace the affine Hecke algebras with the affine Hecke-Clifford
superalgebras of Jones and Nazarov, and the Kac-Moody algebra A_l^(1) with the
twisted algebra A_2l^(2). In particular, we obtain an algebraic construction
purely in terms of the representation theory of Hecke-Clifford superalgebras of
the plus part U_\Z^+ of the enveloping algebra, as well as of Kashiwara's
highest weight crystals B(\infty) and B(\la) for each dominant weight \la.
  The results of the article have applications to the modular representation
theory of the double covers of the symmeric groups, as was predicted originally
by Leclerc and Thibon. In particular, the parametrization of irreducibles,
classification of blocks and analogues of the modular branching rules of the
symmetric group for the double covers over fields of odd characteristic follow
from the special case \lambda = \Lambda_0 of our main results. These matters
are discussed in the final section of the paper.
