Recently Tewari and van Willigenburg constructed modules of the 0-Hecke algebra that are mapped to the quasisymmetric Schur functions by the quasisymmetric characteristic. These modules have a natural decomposition into a direct sum of certain submodules. We show that the summands are indecomposable by determining their endomorphism rings.
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.58
Keywords: 0-Hecke algebra, composition tableau, quasisymmetric function, Schur function
König, Sebastian 1
@article{ALCO_2019__2_5_735_0, author = {K\"onig, Sebastian}, title = {The decomposition of {0-Hecke} modules associated to quasisymmetric {Schur} functions}, journal = {Algebraic Combinatorics}, pages = {735--751}, publisher = {MathOA foundation}, volume = {2}, number = {5}, year = {2019}, doi = {10.5802/alco.58}, zbl = {1421.05092}, mrnumber = {4023564}, language = {en}, url = {https://alco.centre-mersenne.org/articles/10.5802/alco.58/} }
TY - JOUR AU - König, Sebastian TI - The decomposition of 0-Hecke modules associated to quasisymmetric Schur functions JO - Algebraic Combinatorics PY - 2019 SP - 735 EP - 751 VL - 2 IS - 5 PB - MathOA foundation UR - https://alco.centre-mersenne.org/articles/10.5802/alco.58/ DO - 10.5802/alco.58 LA - en ID - ALCO_2019__2_5_735_0 ER -
%0 Journal Article %A König, Sebastian %T The decomposition of 0-Hecke modules associated to quasisymmetric Schur functions %J Algebraic Combinatorics %D 2019 %P 735-751 %V 2 %N 5 %I MathOA foundation %U https://alco.centre-mersenne.org/articles/10.5802/alco.58/ %R 10.5802/alco.58 %G en %F ALCO_2019__2_5_735_0
König, Sebastian. The decomposition of 0-Hecke modules associated to quasisymmetric Schur functions. Algebraic Combinatorics, Volume 2 (2019) no. 5, pp. 735-751. doi : 10.5802/alco.58. https://alco.centre-mersenne.org/articles/10.5802/alco.58/
[1] A lift of the Schur and Hall–Littlewood bases to non-commutative symmetric functions, Canad. J. Math., Volume 66 (2014), pp. 525-565 | DOI | MR | Zbl
[2] Indecomposable modules for the dual immaculate basis of quasi-symmetric functions, Proc. Amer. Math. Soc., Volume 143 (2015), pp. 991-1000 | DOI | MR | Zbl
[3] Skew quasisymmetric Schur functions and noncommutative Schur functions, Adv. Math., Volume 226 (2011), pp. 4492-4532 | DOI | MR | Zbl
[4] Combinatorics of Coxeter groups, Springer Science & Business Media, 2006 | Zbl
[5] Fonctions quasi-symétriques, fonctions symétriques non commutatives et algèbres de Hecke à , C. R. Acad. Sci. Paris Sér. I Math., Volume 322 (1996), pp. 107-112 | Zbl
[6] Multipartite -partitions and inner products of skew Schur functions, Combinatorics and Algebra (Boulder, Colo., 1983) (Contemp. Math.), Volume 34, Amer. Math. Soc., Providence, RI, 1984, pp. 289-317 | DOI | MR | Zbl
[7] Hopf algebras in combinatorics (2014) (https://arxiv.org/abs/1409.8356)
[8] Quasisymmetric Schur functions, J. Combin. Theory Ser. A, Volume 118 (2011), pp. 463-490 | DOI | MR | Zbl
[9] A tableau approach to the representation theory of -Hecke algebras, Ann. Comb., Volume 20 (2016) no. 4, pp. 831-868 | DOI | MR | Zbl
[10] Noncommutative symmetric functions IV: Quantum linear groups and Hecke algebras at , J. Algebraic Combin., Volume 6 (1997), pp. 339-376 | DOI | MR | Zbl
[11] Iwahori–Hecke algebras and Schur algebras of the symmetric group, 15, American Mathematical Soc., 1999 | MR | Zbl
[12] -Hecke algebras, J. Austral. Math. Soc. Ser. A, Volume 27 (1979) no. 3, pp. 337-357 | DOI | MR
[13] Enumerative combinatorics. Vol. 2, Cambridge University Press, Cambridge, 1999, xii+581 pages | Zbl
[14] Modules of the 0-Hecke algebra and quasisymmetric Schur functions, Adv. Math., Volume 285 (2015), pp. 1025-1065 | DOI | MR | Zbl
Cited by Sources: