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Let K be an algebraically closed field of characteristic 0, and let E be the infinite dimensional Grassmann (or exterior) algebra over K. Denote by P-n the vector space of the multilinear polynomials of degree n in x(1), ..., x(n) in the free associative algebra K(X). The symmetric group S-n acts on the left-hand side on P-n, thus turning it into an S-n-module. This fact, although simple, plays an important role in the theory of PI algebras since one may study the identities satisfied by a given algebra by applying methods from the representation theory of the symmetric group. The S-n-modules P-n and KSn are canonically isomorphic. Letting An be the alternating group in S-n, one may study KA(n) and its isomorphic copy in P-n with the corresponding action of A(n). Henke and Regev described the A(n)-codimensions of the Grassmann algebra E, and conjectured a finite generating set of the A(n)-identities for E. Here we answer their conjecture in the affirmative

$A$-identities for the Grassmann algebra: The conjecture of Henke and Regev