9 papers
The Antipodes of -Quasi-Symmetric Functions and Non-Commutative Quasi-Symmetric Functions
Shaul Zemel
We prove the antipode formula for the -deformations of quasi-symmetric functions. We also define a fundamental basis for non-commutative quasi-symmetric functions, and establish…
Polynomial Expressions for Symmetric Group Characters on Cycles
Tom Moshaiov, Shaul Zemel
In \cite{[CZ]}, Cohen and Zemel showed that for a partition , the dimension of the irreducible representation of corresponding to the partition $(n-k,λ) \vdash…
Stable Higher Specht Polynomials and Representations of Infinite Symmetric Groups
Shaul Zemel
We define eventually symmetric functions to be those power series of bounded degree in infinitely many variables that are invariant under interchanging all the variables with large…
Generalized Higher Specht Polynomials and Homogeneous Representations of Symmetric Groups
Shaul Zemel
We consider actions, similar to those of Haglund, Rhoades, and Shimozono on ordered partitions, and their basis in terms of the higher Specht polynomials of Ariki, Terasoma, and Ya…
Compatibility of Higher Specht Polynomials and Decompositions of Representations
Shaul Zemel
%We show how to normalize the higher Specht polynomials of Ariki, Terasoma, and Yamada in a compatible way in order to define a stable version of these polynomials. We also decompo…
Generating Series of Key Polynomials and Bounded Ascending Sequences of Integers
Noah Cape, Shaul Zemel
The fact that Schubert polynomials are the weighted counting functions for reduced RC-graphs, also known as reduced pipe dreams, was established using their generating functions in…