Skew Schur Functions and Yangian Actions on Irreducible Integrable Modules of $ \hat{\frak g \frak l} _N $

2000 ◽  
Vol 4 (3) ◽  
pp. 383-400 ◽  
Author(s):  
Denis Uglov
Keyword(s):  
Schur Functions ◽  
Skew Schur Functions ◽  
Integrable Modules

scholarly journals Coincidences among skew Schur functions

2007 ◽  
Vol 216 (1) ◽  
pp. 118-152 ◽  
Author(s):  
Victor Reiner ◽  
Kristin M. Shaw ◽  
Stephanie van Willigenburg
Keyword(s):  
Schur Functions ◽  
Skew Schur Functions

scholarly journals Staircase skew Schur functions are Schur P-positive

2012 ◽  
Vol 36 (3) ◽  
pp. 409-423 ◽  
Author(s):  
Federico Ardila ◽  
Luis G. Serrano
Keyword(s):  
Schur Functions ◽  
Skew Schur Functions

scholarly journals Skew Littlewood―Richardson rules from Hopf algebras

2010 ◽  
Vol DMTCS Proceedings vol. AN,... (Proceedings) ◽  
Author(s):  
Thomas Lam ◽  
Aaron Lauve ◽  
Frank Sottile
Keyword(s):  
Hopf Algebras ◽  
Symplectic Group ◽  
Schur Functions ◽  
Affine Grassmannian ◽  
International Audience ◽  
Pieri Rules ◽  
Skew Schur Functions ◽  
Nous Utilisons

International audience We use Hopf algebras to prove a version of the Littlewood―Richardson rule for skew Schur functions, which implies a conjecture of Assaf and McNamara. We also establish skew Littlewood―Richardson rules for Schur $P-$ and $Q-$functions and noncommutative ribbon Schur functions, as well as skew Pieri rules for k-Schur functions, dual k-Schur functions, and for the homology of the affine Grassmannian of the symplectic group. Nous utilisons des algèbres de Hopf pour prouver une version de la règle de Littlewood―Richardson pour les fonctions de Schur gauches, qui implique une conjecture d'Assaf et McNamara. Nous établissons également des règles de Littlewood―Richardson gauches pour les $P-$ et $Q-$fonctions de Schur et les fonctions de Schur rubbans non commutatives, ainsi que des règles de Pieri gauches pour les $k-$fonctions de Schur, les $k-$fonctions de Schur duales, et pour l'homologie de la Grassmannienne affine du groupe symplectique.

scholarly journals Cylindric skew Schur functions

2006 ◽  
Vol 205 (1) ◽  
pp. 275-312 ◽  
Author(s):  
Peter McNamara
Keyword(s):  
Schur Functions ◽  
Skew Schur Functions

scholarly journals Double Posets and the Antipode of QSym

10.37236/6660 ◽  
2017 ◽  
Vol 24 (2) ◽  
Author(s):  
Darij Grinberg
Keyword(s):  
Weight Function ◽  
Schur Functions ◽  
Second Order ◽  
Partial Orders ◽  
Quasisymmetric Function ◽  
Quasisymmetric Functions ◽  
Finite Set ◽  
Skew Schur Functions

A quasisymmetric function is assigned to every double poset (that is, every finite set endowed with two partial orders) and any weight function on its ground set. This generalizes well-known objects such as monomial and fundamental quasisymmetric functions, (skew) Schur functions, dual immaculate functions, and quasisymmetric $\left(P, \omega\right)$-partition enumerators. We prove a formula for the antipode of this function that holds under certain conditions (which are satisfied when the second order of the double poset is total, but also in some other cases); this restates (in a way that to us seems more natural) a result by Malvenuto and Reutenauer, but our proof is new and self-contained. We generalize it further to an even more comprehensive setting, where a group acts on the double poset by automorphisms.

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