15 citations · 104 across the 38 of their papers we have counts for
40 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 n…
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…
Polynomial Expressions for the Dimensions of the Representations of Symmetric Groups and Restricted Standard Young Tableaux
Avichai Cohen, Shaul Zemel
Given a partition of a number , it is known that by adding a long line of length , the dimension of the associated representation of is an integer-valued polyno…
Polynomial Divided Difference Operators Satisfying the Braid Relations
Shaul Zemel
Many interesting families of polynomials are indexed by permutations or related objects, and are defined by applying divided difference operators, modified by polynomials, on some…
Modularity of special 0-cycles on toroidal compactifications of Shimura Varieties
Jan Hendrik Bruinier, Eugenia Rosu, Shaul Zemel
We consider the generating series of appropriately completed 0-dimensional special cycles on a toroidal compactification of an orthogonal or unitary Shimura variety with values in…
Hermitian Jacobi Forms Having Modules as their Index and Vector-Valued Jacobi Forms
Shaul Zemel
We develop the theory of Hermitian Jacobi forms of lattice index, for both definite and indefinite Hermitian lattices. We also prove a theta decomposition theorem for vector-valued…
On Differentiating Symmetric Functions
Shaul Zemel
A symmetric function of variables can be given in terms of symmetric polynomials of these variables. We determine those symmetric polynomials in which the dual differential ope…
On Higher Partial Derivatives of Implicit Functions and their Combinatorics
Shaul Zemel
We consider a scalar-valued implicit function of many variables, and provide two closed formulae for all of its partial derivatives. One formula is based on products of partial der…
Generalized Hyperbolic Spaces Associated with Arbitrary Quadratic Forms
Shaul Zemel
The Vahlen group gives a way for presenting the hyperbolic space of every dimension of a group acting via Möbius transformations. As Vahlen groups and paravector Vahlen groups are…
Clifford Groups of Arbitrary Quadratic Modules over Commutative Rings
Shaul Zemel
We consider the Clifford algebra and the Clifford group associated with any quadratic module, degenerate or not, over an arbitrary commutative ring with 1. We determine some of the…
Integral Bases and Invariant Vectors for Weil Representations
Shaul Zemel
We show that the Weil representation associated with any discriminant form admits a basis in which the action of the representation involves algebraic integers. The action of a gen…
Shintani Lifts of Nearly Holomorphic Modular Forms
Yingkun Li, Shaul Zemel
In this paper, we compute the Fourier expansion of the Shintani lift of nearly holomorphic modular forms. As an application, we deduce modularity properties of generating series of…
Seesaw Identities and Theta Contractions with Generalized Theta Functions, and Restrictions of Theta Lifts
Shaul Zemel
We prove a seesaw identity for theta functions with polynomials, and establish a formula for the corresponding theta contractions. We then use it to determine the restrictions of t…
Jacobi Forms of Indefinite Lattice Index
Shaul Zemel
We define Jacobi forms of indefinite lattice index, and show that they are isomorphic to vector-valued modular forms also in this setting. We also consider several operations of th…
Moments of Partitions and Derivatives of Higher Order
Shaul Zemel
We Define moments of partitions of integers, and show that they appear in higher order derivatives of certain combinations of functions.
Special Cycles on Toroidal Compactifications of Orthogonal Shimura Varieties
Jan Hendrik Bruinier, Shaul Zemel
We determine the behavior of automorphic Green functions along the boundary components of toroidal compactifications of orthogonal Shimura varieties. We use this analysis to define…
The Structure of Integral Parabolic Subgroups of Orthogonal Groups
Shaul Zemel
We determine the detailed structure of parabolic subgroups of orthogonal groups over , and deduce the precise form of canonical boundary components in toroidal compacti…
Thomae's Derivative Formulae for Trigonal Curves
Victor Enolski, Yaacov Kopeliovich, Shaul Zemel
In this paper we prove a Thomae derivative formula for trigonal curves admitting a non-singular affine model. This formula relates the derivatives of theta functions with rational…
The Combinatorics of Higher Derivatives of Implicit Functions
Shaul Zemel
We prove a closed formula for the derivative, of any order, of a implicit function, in terms of some binomial building blocks, and explain the combinatorics behind the coefficients…
The Origin of the Beauregard--Suryanarayan Product on Pythagorean Triples
Shaul Zemel
We show how the multiplicative structure on Pythagorean triples defined by Beauregard--Suryanarayan arises from automorphisms of the hyperbolic plane, and how the structure theorem…