The peak algebra and the Hecke-Clifford algebras at $q=0$

Abstract

Using the formalism of noncommutative symmetric functions, we derive the basic theory of the peak algebra of symmetric groups and of its graded Hopf dual. Our main result is to provide a representation theoretical interpretation of the peak algebra and its graded dual as Grothendieck rings of the tower of Hecke-Clifford algebras at $q=0$.

Final version, 17 pages, LaTex, 1 PDF figure, graphicx

References in corpus (2)

• The peak algebra and the descent algebras of types B and D
• q and q,t-Analogs of Non-commutative Symmetric Functions

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• Extending the descent-to-peak map and its applications
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• Quasisymmetric Schur $Q$-functions and peak Young quasisymmetric Schur functions
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