pieri rules
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2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Masaki Watanabe

International audience In their 1987 paper Kraskiewicz and Pragacz defined certain modules, which we call KP modules, over the upper triangular Lie algebra whose characters are Schubert polynomials. In a previous work the author showed that the tensor product of Kraskiewicz-Pragacz modules always has KP filtration, i.e. a filtration whose each successive quotients are isomorphic to KP modules. In this paper we explicitly construct such filtrations for certain special cases of these tensor product modules, namely Sw Sd(Ki) and Sw Vd(Ki), corresponding to Pieri and dual Pieri rules for Schubert polynomials.





10.37236/8174 ◽  
2019 ◽  
Vol 26 (3) ◽  
Author(s):  
Wanwan Jia ◽  
Zhengpan Wang ◽  
Houyi Yu

We investigate the rigidity for the Hopf algebra QSym of quasisymmetric functions with respect to the monomial, the fundamental and the quasisymmetric Schur basis, respectively. By establishing some combinatorial properties of the posets of compositions arising from the analogous Pieri rules for quasisymmetric functions, we show that QSym is rigid as an algebra with respect to the quasisymmetric Schur basis, and rigid as a coalgebra with respect to the monomial and the quasisymmetric Schur basis, respectively. The natural actions of reversal, complement and transpose of the labelling compositions lead to some nontrivial graded (co)algebra automorphisms of QSym. We prove that the linear maps induced by the three actions are precisely the only nontrivial graded algebra automorphisms that take the fundamental basis into itself. Furthermore, the complement map on the labels gives the unique nontrivial graded coalgebra automorphism preserving the fundamental basis, while the reversal map on the labels gives the unique nontrivial graded algebra automorphism preserving the monomial basis. Therefore, QSym is rigid as a Hopf algebra with respect to the monomial and the quasisymmetric Schur basis.



2019 ◽  
Vol 20 (4) ◽  
pp. 1051-1091 ◽  
Author(s):  
Jessica Gatica ◽  
Miles Jones ◽  
Luc Lapointe


2018 ◽  
Vol 100 ◽  
pp. 101-121 ◽  
Author(s):  
Vasu Tewari ◽  
Stephanie van Willigenburg
Keyword(s):  


2017 ◽  
Vol 148 ◽  
pp. 57-115 ◽  
Author(s):  
Miles Jones ◽  
Luc Lapointe
Keyword(s):  


10.37236/6214 ◽  
2016 ◽  
Vol 23 (4) ◽  
Author(s):  
Soichi Okada

We present several equinumerous results between generalized oscillating tableaux and semistandard tableaux and give a representation-theoretic proof to them. As one of the key ingredients of the proof, we provide Pieri rules for the symplectic and orthogonal groups.



Author(s):  
Adriano Garsia ◽  
Jim Haglund ◽  
Guoce Xin ◽  
Mike Zabrocki
Keyword(s):  


2016 ◽  
Vol 49 (15) ◽  
pp. 154006 ◽  
Author(s):  
Antoine Duval ◽  
Vincent Pasquier
Keyword(s):  


2015 ◽  
Vol 365 (1-2) ◽  
pp. 881-909 ◽  
Author(s):  
Changzheng Li ◽  
Vijay Ravikumar
Keyword(s):  


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