The Howe duality and the Projective Representations of Symmetric Groups

Details The Howe duality and the Projective Representations of Symmetric Groups The Howe duality and the Projective Representations of Symmetric Groups

1998-10-27

arxiv.org/abs/math/9810148v1

Mathematics

Representation Theory

9 p., Latex

Scientific paper

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

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