190 citations · 561 across the 46 of their papers we have counts for
10 papers · 1 filter
Connections between vector-valued and highest weight Jack and Macdonald polynomials
Laura Colmenarejo, Charles F. Dunkl, Jean-Gabriel Luque
We analyze conditions under which a projection from the vector-valued Jack or Macdonald polynomials to scalar polynomials has useful properties, especially commuting with the actio…
Factorizations of symmetric Macdonald polynomials
Laura Colmenarejo, Charles F. Dunkl, Jean-Gabriel Luque
We prove many factorization formulas for highest weight Macdonald polynomials indexed by particular partitions called quasistaircases. As a consequence we prove a conjecture of Ber…
Entanglement of four-qubit systems: a geometric atlas with polynomial compass II (the tame world)
Frédéric Holweck, Jean-Garbriel Luque, Jean-Yves Thibon
We propose a new approach to the geometry of the four-qubit entanglement classes depending on parameters. More precisely, we use invariant theory and algebraic geometry to describe…
Singularity of type arising from four qubit systems
Frédéric Holweck, Jean-Gabriel Luque, Michel Planat
An intriguing correspondence between four-qubit systems and simple singularity of type is established. We first consider an algebraic variety of separable states within t…
Entanglement of four qubit systems: a geometric atlas with polynomial compass I (the finite world)
Frédéric Holweck, Jean-Gabriel Luque, Jean-Yves Thibon
We investigate the geometry of the four qubit systems by means of algebraic geometry and invariant theory, which allows us to interpret certain entangled states as algebraic variet…
Geometric descriptions of entangled states by auxiliaries varieties
Frédéric Holweck, Jean-Gabriel Luque, Jean-Yves Thibon
The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of t…