0-Hecke algebra action on the Stanley-Reisner ring of the Boolean algebra

Abstract

We define an action of the 0-Hecke algebra of type A on the Stanley-Reisner ring of the Boolean algebra. By studying this action we obtain a family of multivariate noncommutative symmetric functions, which specialize to the noncommutative Hall-Littlewood symmetric functions and their (q,t)-analogues introduced by Bergeron and Zabrocki, and to a more general family of noncommutative symmetric functions having parameters associated with paths in binary trees introduced recently by Lascoux, Novelli, and Thibon. We also obtain multivariate quasisymmetric function identities, which specialize to results of Garsia and Gessel on generating functions of multivariate distributions of permutation statistics.

arXiv commentAdded connections with a family of noncommutative symmetric functions introduced recently by Lascoux, Novelli, and Thibon

References in corpus (5)

• Algebraic Structures on Grothendieck Groups of a Tower of Algebras
• q and q,t-Analogs of Non-commutative Symmetric Functions
• Oddification of the cohomology of type A Springer varieties
• Noncommutative symmetric functions and quasi-symmetric functions with two and more paramters
• Noncommutative symmetric functions with matrix parameters

Cited by in corpus (6)

• Labeled binary trees, subarrangements of the Catalan arrangements, and Schur positivity
• A tableau approach to the representation theory of 0-Hecke algebras
• Artin group injection in the Hecke algebra for right-angled groups
• Representation stability for sequences of 0-Hecke modules
• Hecke algebras of simply-laced type with independent parameters
• Modules of the 0-Hecke algebra and quasisymmetric Schur functions