  Young's orthogonal basis is a classical basis for an irreducible
representation of a symmetric group. This basis happens to be a Gelfand-Tsetlin
basis for the chain of symmetric groups. It is well-known that the chain of
alternating groups, just like the chain of symmetric groups, has
multiplicity-free restrictions for irreducible representations. Therefore each
irreducible representation of an alternating group also admits Gelfand-Tsetlin
bases. Moreover, each such representation is either the restriction of, or a
subrepresentation of, the restriction of an irreducible representation of a
symmetric group. In this article, we describe a recursive algorithm to write
down the expansion of each Gelfand-Tsetlin basis vector for an irreducible
representation of an alternating group in terms of Young's orthogonal basis of
the ambient representation of the symmetric group. This algorithm is
implemented with the Sage Mathematical Software.
