The Howe duality and the Projective Representations of Symmetric Groups

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The symmetric group Sₙ possesses a nontrivial central extension, whose irreducible representations, different from the irreducible representations of Sₙ itself, coincide with the irreducible representations of a certain algebra Aₙ. Recently M. Nazarov realized irreducible representations of Aₙ and Young symmetrizers by means of the Howe duality between the Lie superalgebra q(n) and the Hecke algebra Hₙ, the semidirect product of Sₙ with the Clifford algebra Cₙ on n indeterminates. Here I construct one more analog of Young symmetrizers in Hₙ as well as the analogs of Specht modules for Aₙ and Hₙ.