The Howe duality

and the projective representations

of symmetric groups

Author:
Alexander Sergeev

Journal:
Represent. Theory **3** (1999), 416-434

MSC (1991):
Primary 20C30, 20C25, 17A70

DOI:
https://doi.org/10.1090/S1088-4165-99-00085-0

Published electronically:
November 9, 1999

MathSciNet review:
1722115

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The symmetric group possesses a nontrivial central extension, whose irreducible representations, different from the irreducible representations of itself, coincide with the irreducible representations of the algebra generated by indeterminates for , subject to the relations

Recently M. Nazarov realized irreducible representations of and Young symmetrizers by means of the Howe duality between the Lie superalgebra and the Hecke algebra , the semidirect product of with the Clifford algebra on indeterminates.

Here I construct one more analog of Young symmetrizers in as well as the analogs of Specht modules for and .

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Additional Information

**Alexander Sergeev**

Affiliation:
On leave of absence from Balakovo Institute of Technique of Technology and Control, Branch of Saratov State Technical University, Russia;
Department of Mathematics, University of Stockholm, Roslagsv. 101, Kräftriket hus 6, S-106 91, Stockholm, Sweden

Email:
mleites@matematik.su.se (subject: for Sergeev)

DOI:
https://doi.org/10.1090/S1088-4165-99-00085-0

Keywords:
Projective representations,
symmetric group,
Howe duality

Received by editor(s):
September 4, 1998

Received by editor(s) in revised form:
September 8, 1999

Published electronically:
November 9, 1999

Additional Notes:
I am thankful to D. Leites for support; to him and the referee for help

Article copyright:
© Copyright 1999
American Mathematical Society