1 citations · 1 across the 11 of their papers we have counts for
11 papers
Eigenvalues of locally positive semidefinite matrices: Non-convexity and Geometry
Jose Acevedo, Grigoriy Blekherman, Sebastian Debus +2
A real symmetric matrix is called -locally positive semidefinite if all of its principal submatrices are positive semidefinite. We investigate the spectral geometry…
Any-dimensional Positivstellensätze for symmetric functions
Sebastian Debus, Robin Schabert
Positivstellensätze provide certificates of positivity for polynomials. Extending these certificates to symmetric functions, uniformly across all dimensions, presents structural ch…
Posets for Specht ideals of essential real reflection groups
Sebastian Debus, Kurt Klement Gottwald
Specht ideals are symmetric ideals in the polynomial ring generated by Specht polynomials associated with group representations. These ideals were previously studied for reflection…
Additive and Multiplicative Coinvariant Spaces of Weyl Groups in the Light of Harmonics and Graded Transfer
Sebastian Debus, Tobias Metzlaff
The action of a Weyl group on the associated weight lattice induces an additive action on the symmetric algebra and a multiplicative action on the group algebra of the lattice. We…
Symmetric nonnegative functions, the tropical Vandermonde cell and superdominance of power sums
Jose Acevedo, Grigoriy Blekherman, Sebastian Debus +1
We study nonnegative and sums of squares symmetric (and even symmetric) functions of fixed degree. We can think of these as limit cones of symmetric nonnegative polynomials and sym…
Symmetric Ideals and Invariant Hilbert Schemes
Sebastian Debus, Andreas Kretschmer
A symmetric ideal is an ideal in a polynomial ring which is stable under all permutations of the variables. In this paper we initiate a global study of zero-dimensional symmetric i…
On nonnegative invariant quartics in type A
Sebastian Debus, Charu Goel, Salma Kuhlmann +1
The equivariant nonnegativity versus sums of squares question has been solved for any infinite series of essential reflection groups but type A. As a first step to a classification…
Slices of Stable Polynomials and Connections to the Grace-Walsh-Szegő theorem
Sebastian Debus, Cordian Riener, Robin Schabert
Univariate polynomials are called stable with respect to a domain if all of their roots lie in . We study linear slices of the space of stable univariate polynomials with re…
The Wonderful Geometry of the Vandermonde map
Jose Acevedo, Grigoriy Blekherman, Sebastian Debus +1
We study the geometry of the image of the nonnegative orthant under the power-sum map and the elementary symmetric polynomials map. After analyzing the image in finitely many varia…
The poset of Specht ideals for hyperoctahedral groups
Sebastian Debus, Philippe Moustrou, Cordian Riener +1
Specht polynomials classically realize the irreducible representations of the symmetric group. The ideals defined by these polynomials provide a strong connection with the combinat…
Reflection groups and cones of sums of squares
Sebastian Debus, Cordian Riener
We consider cones of real forms which are sums of squares forms and invariant by a (finite) reflection group. We show how the representation theory of these groups allows to use th…