Publications (22)
Macdonald polynomials in superspace: conjectural definition and positivity conjectures
O. Blondeau-Fournier, P. Desrosiers, L. Lapointe +1
We introduce a conjectural construction for an extension to superspace of the Macdonald polynomials. The construction, which depends on certain orthogonality and triangularity rela…
Supersymmetric Calogero-Moser-Sutherland models and Jack superpolynomials
P. Desrosiers, L. Lapointe, P. Mathieu
A new generalization of the Jack polynomials that incorporates fermionic variables is presented. These Jack superpolynomials are constructed as those eigenfunctions of the supersym…
Tableaux on k+1-cores, reduced words for affine permutations, and k-Schur expansions
L. Lapointe, J. Morse
The -Young lattice is a partial order on partitions with no part larger than . This weak subposet of the Young lattice originated from the study of the -Schur functi…
Schur function identities, their t-analogs, and k-Schur irreducibility
L. Lapointe, J. Morse
We obtain general identities for the product of two Schur functions in the case where one of the functions is indexed by a rectangular partition, and give their t-analogs using ver…
Pieri rules for the Jack polynomials in superspace and the 6-vertex model
J. Gatica, M. Jones, L. Lapointe
We present Pieri rules for the Jack polynomials in superspace. The coefficients in the Pieri rules are, except for an extra determinant, products of quotients of linear factors in…
Fusion bases as facets of polytopes
L. Bégin, C. Cummins, L. Lapointe +1
A new way of constructing fusion bases (i.e., the set of inequalities governing fusion rules) out of fusion elementary couplings is presented. It relies on a polytope reinterpretat…
Bernstein operators and super-Schur functions: combinatorial aspects
L. Alarie-Vézina, O. Blondeau-Fournier, L. Lapointe +1
The Bernstein vertex operators, which can be used to build recursively the Schur functions, are extended to superspace. Four families of super vertex operators are defined, corresp…
Symmetric functions in superspace
P. Desrosiers, L. Lapointe, P. Mathieu
We construct a generalization of the theory of symmetric functions involving functions of commuting and anticommuting (Grassmannian) variables. These new functions, called symmetri…
Quantum cohomology and the k-Schur basis
L. Lapointe, J. Morse
We prove that structure constants related to Hecke algebras at roots of unity are special cases of k-Littlewood-Richardson coefficients associated to a product of k-Schur functions…
N>=2 symmetric superpolynomials
L. Alarie-Vézina, L. Lapointe, P. Mathieu
The theory of symmetric functions has been extended to the case where each variable is paired with an anticommuting one. The resulting expressions, dubbed superpolynomials, provide…
Tableaux statistics for two part Macdonald polynomials
L. Lapointe, J. Morse
The Macdonald polynomials expanded in terms of a modified Schur function basis have coefficients called the -Kostka polynomials. We define operators to build standard tableaux…
Tableau atoms and a new Macdonald positivity conjecture
L. Lapointe, A. Lascoux, J. Morse
Let be the space of symmetric functions and be the subspace spanned by the modified Schur functions . We introduce a new family of symmet…
Supersymmetric Calogero-Moser-Sutherland models: superintegrability structure and eigenfunctions
P. Desrosiers, L. Lapointe, P. Mathieu
We first review the construction of the supersymmetric extension of the (quantum) Calogero-Moser-Sutherland (CMS) models. We stress the remarkable fact that this extension is compl…
Determinantal expressions for Macdonald polynomials
L. Lapointe, A. Lascoux, J. Morse
We show that the action of classical operators associated to the Macdonald polynomials on the basis of Schur functions, S_λ[X(t-1)/(q-1)], can be reduced to addition in λ-rings.…
Magnetic structure of GdBiPt: A candidate antiferromagnetic topological insulator
R. A. Müller, N. R. Lee-Hone, L. Lapointe +5
A topological insulator is a state of matter which does not break any symmetry and is characterized by topological invariants, the integer expectation values of non-local operators…
Double Macdonald polynomials as the stable limit of Macdonald superpolynomials
O. Blondeau-Fournier, L. Lapointe, P. Mathieu
Macdonald superpolynomials provide a remarkably rich generalization of the usual Macdonald polynomials. The starting point of this work is the observation of a previously unnoticed…
Jack polynomials in superspace
P. Desrosiers, L. Lapointe, P. Mathieu
This work initiates the study of {\it orthogonal} symmetric polynomials in superspace. Here we present two approaches leading to a family of orthogonal polynomials in superspace th…
Super-Whittaker vector at c=3/2
P. Desrosiers, L. Lapointe, P. Mathieu
The degenerate Whittaker vector of the superconformal algebra can be represented in terms of Jack superpolynomials. However, in this representation the norm of the Whittaker vector…
Jack superpolynomials, superpartition ordering and determinantal formulas
P. Desrosiers, L. Lapointe, P. Mathieu
We call superpartitions the indices of the eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland model. We obtain an ordering on superpartit…
Magnetic structure of the antiferromagnetic half-Heusler compound NdBiPt
R. A. Mueller, A. Desilets-Benoit, N. Gauthier +9
We present results of single crystal neutron diffraction experiments on the rare-earth, half-Heusler antiferromagnet (AFM) NdBiPt. This compound exhibits an AFM phase transition at…
Macdonald polynomials in superspace as eigenfunctions of commuting operators
O. Blondeau-Fournier, P. Desrosiers, L. Lapointe +1
A generalization of the Macdonald polynomials depending upon both commuting and anticommuting variables has been introduced recently. The construction relies on certain orthogonali…
Schur function analogs for a filtration of the symmetric function space
L. Lapointe, J. Morse
We consider a filtration of the symmetric function space given by , the linear span of Hall-Littlewood polynomials indexed by partitions whose first part is not larger…