q and q,t-Analogs of Non-commutative Symmetric Functions

Abstract

We introduce two families of non-commutative symmetric functions that have analogous properties to the Hall-Littlewood and Macdonald symmetric functions.

Different from analogues in math.CO/0106191 - v2: 26 pages - added a definition in terms of triangularity/scalar product relations - to be submitted FPSAC'02

References in corpus (1)

• Noncommutative symmetric functions and quasi-symmetric functions with two and more paramters

Cited by in corpus (8)

• A lift of the Schur and Hall-Littlewood bases to non-commutative symmetric functions
• The peak algebra and the Hecke-Clifford algebras at $q=0$
• 0-Hecke algebra action on the Stanley-Reisner ring of the Boolean algebra
• Noncommutative Analogs of Monomial Symmetric Functions, Cauchy Identity, and Hall Scalar Product
• On some noncommutative symmetric functions analogous to Hall-Littlewood and Macdonald polynomials
• Noncommutative symmetric functions with matrix parameters
• Combinatorial Hopf algebras, noncommutative Hall-Littlewood functions, and permutation tableaux
• A non-commutative generalization of $k$-Schur functions