  We introduce ``virtual'' crystals of the affine types $g=D_{n+1}^{(2)}$,
$A_{2n}^{(2)}$ and $C_n^{(1)}$ by naturally extending embeddings of crystals of
types $B_n$ and $C_n$ into crystals of type $A_{2n-1}$. Conjecturally, these
virtual crystals are the crystal bases of finite dimensional $U_q'(g)$-modules
associated with multiples of fundamental weights. We provide evidence and in
some cases proofs of this conjecture. Recently, fermionic formulas for the one
dimensional configuration sums associated with tensor products of the finite
dimensional $U_q'(g)$-modules were conjectured by Hatayama et al. We provide
proofs of these conjectures in specific cases by exploiting duality properties
of crystals and rigged configuration techniques. For type $A_{2n}^{(2)}$ we
also conjecture a new fermionic formula coming from a different labeling of the
Dynkin diagram.

Quantum Algebra