We formulate a theory of invariants for the spin symmetric group in some
suitable modules which involve the polynomial and exterior algebras. We solve
the corresponding graded multiplicity problem in terms of specializations of
the Schur Q-functions and a shifted q-hook formula. In addition, we provide a
bijective proof for a formula of the principal specialization of the Schur
Q-functions.Comment: v2, 17 pages, modified Introduction and updated references. v3,
  correction of typos, final versio

Wan, Jinkui