Skew row-strict quasisymmetric Schur functions

Mason, Sarah; Niese, Elizabeth

doi:10.1007/s10801-015-0601-6

Cited by 13 publications

(18 citation statements)

References 22 publications

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“…The quasisymmetric (2, 2)-hook Schur function HQ (1,2,1) (x 1 , x 2 ; y 1 , y 2 ). functions [MR14,MN15]. In particular,…”

Section: Properties Of the Quasisymmetric (K L)-hook Schur Functionsmentioning

confidence: 99%

“…Both the column-strict and row-strict quasisymmetric functions can be decomposed as sums of fundamental quasisymmetric functions as shown in [LMvW13,MN15]. Let D ⊆ [n − 1].…”

Section: Super Fundamental Quasisymmetric Functionsmentioning

confidence: 99%

“…We will again work with the variation, RS α , of the row-strict quasisymmetric functions obtained by the same reversal procedure as is employed in [LMvW13]. In fact, we further extend this approach to include skew compositions as indexing compositions as in [MN15].…”

Section: Introductionmentioning

confidence: 99%

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Quasisymmetric (k, l)-Hook Schur Functions

Mason

Niese

2018

Ann. Comb.

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We introduce a quasisymmetric generalization of Berele and Regev's hook Schur functions and prove that these new quasisymmetric hook Schur functions decompose the hook Schur functions in a natural way. We examine the combinatorics of the quasisymmetric hook Schur functions, providing a relationship to Gessel's fundamental quasisymmetric functions and an analogue of the Robinson-Schensted-Knuth algorithm. We also prove that the multiplication of quasisymmetric hook Schur functions with hook Schur functions behaves the same as the multiplication of quasisymmetric Schur functions with Schur functions.

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“…The quasisymmetric (2, 2)-hook Schur function HQ (1,2,1) (x 1 , x 2 ; y 1 , y 2 ). functions [MR14,MN15]. In particular,…”

Section: Properties Of the Quasisymmetric (K L)-hook Schur Functionsmentioning

confidence: 99%

“…Both the column-strict and row-strict quasisymmetric functions can be decomposed as sums of fundamental quasisymmetric functions as shown in [LMvW13,MN15]. Let D ⊆ [n − 1].…”

Section: Super Fundamental Quasisymmetric Functionsmentioning

confidence: 99%

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Quasisymmetric (k, l)-Hook Schur Functions

Mason

Niese

2018

Ann. Comb.

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“…The area of Schur-like functions began with quasisymmetric Schur functions [12], followed by discoveries of row-strict quasisymmetric Schur functions [16], Young quasisymmetric Schur functions [15,17], noncommutative Schur functions [6] and immaculate functions [4], quasisymmetric Schur Q-functions [14], quasisymmetric Macdonald polynomials [8], and Schur functions in noncommuting variables [1].…”

mentioning

confidence: 99%

0-Hecke modules for row-strict dual immaculate functions

Niese¹,

Sundaram²,

Willigenburg³

et al. 2022

Preprint

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We introduce a new basis of quasisymmetric functions, the row-strict dual immaculate functions. We construct a cyclic, indecomposable 0-Hecke algebra module for these functions. Our row-strict immaculate functions are related to the dual immaculate functions of Berg-Bergeron-Saliola-Serrano-Zabrocki (2014-15) by the involution ψ on the ring QSym of quasisymmetric functions. We give an explicit description of the effect of ψ on the associated 0-Hecke modules, via the poset induced by the 0-Hecke action on standard immaculate tableaux. This remarkable poset reveals other 0-Hecke submodules and quotient modules, often cyclic and indecomposable, notably for a row-strict analogue of the extended Schur functions studied in Assaf-Searles (2019).Like the dual immaculate function, the row-strict dual immaculate function is the generating function of a suitable set of tableaux, corresponding to a specific descent set. We give a complete combinatorial and representation-theoretic picture by constructing 0-Hecke modules for the remaining variations on descent sets, and showing that all the possible variations for generating functions of tableaux occur as characteristics of the 0-Hecke modules determined by these descent sets.

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“…A common framework for 0-Hecke modules for bases of QSym Recently, many families of H n p0q-modules have been constructed so that their images under the quasisymmetric characteristic map are noteworthy bases of QSym. This has been done in [6] for the dual immaculate functions introduced in [5], in [38] for the quasisymmetric Schur functions introduced in [18], in [34] for the extended Schur functions introduced in [3], in [4] for the Young row-strict quasisymmetric Schur functions introduced in [29], and in [31] for the row-strict extended Schur functions and also for the row-strict dual immaculate functions introduced in [30]. In each case, the module is defined on the span of a family of standard tableaux whose underlying shapes are diagrams of compositions.…”

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confidence: 99%

Diagram supermodules for $0$-Hecke-Clifford algebras

Searles¹

2022

Preprint

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We introduce a general method for constructing modules for 0-Hecke algebras and supermodules for 0-Hecke-Clifford algebras from diagrams of boxes in the plane, and give formulas for the images of these modules in the algebras of quasisymmetric functions and peak functions under the relevant characteristic map. As initial applications, we resolve a question of Jing and Li (2015), introduce a new basis of the peak algebra analogous to the quasisymmetric Schur functions, uncover a new connection between Schur Q-functions and quasisymmetric Schur functions, give a representation-theoretic interpretation of families of tableaux used in constructing certain functions in the peak algebra, and establish a common framework for known 0-Hecke module interpretations of bases of quasisymmetric functions.

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Skew row-strict quasisymmetric Schur functions

Cited by 13 publications

References 22 publications

Quasisymmetric (k, l)-Hook Schur Functions

Quasisymmetric (k, l)-Hook Schur Functions

0-Hecke modules for row-strict dual immaculate functions

Diagram supermodules for $0$-Hecke-Clifford algebras

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