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We determine set-theoretic defining equations for the variety Dual k,d,N ⊂ P(S d C N) of hypersurfaces of degree d in C N that have dual variety of dimension at most k. We apply these equations to the Mulmuley-Sohoni variety GL n 2 · [detn] ⊂ P(S n C n 2), showing it is an irreducible component of the variety of hypersurfaces of degree n in C n 2 with dual… (More)

- N Ressayre
- 2009

Let G be a connected reductive subgroup of a complex connected reductive groupˆG. Fix maximal tori and Borel subgroups of G andˆG. Consider the cone LR(ˆ G, G) generated by the pairs (ν, ˆ ν) of dominant characters such that V ν is a submodule of V ˆ ν (with usual notation). Here we give a minimal set of inequalities describing LR(ˆ G, G) as a part of the… (More)

Grenet's determinantal representation for the permanent is optimal among determinantal representations that are equivariant with respect to left multiplication by permutation and diagonal matrices (roughly half the symmetry group of the permanent). In particular, if any optimal determinantal representation of the permanent must be polynomially related to… (More)

- Pl Montagard, B Pasquier, N Ressayre
- 2011

Let G ⊂ ˆ G be two complex connected reductive groups. We deals with the hard problem of finding sub-G-modules of a given irreduciblê G-module. In the case where G is diagonally embedded inˆG = G × G, S. Kumar and O. Mathieu found some of them, proving the PRV conjecture. Recently, the authors generalized the PRV conjecture on the one hand to the case wherê… (More)

- N Ressayre
- 2009

Let G be a complex connected reductive algebraic group and G/B denote the flag variety of G. A G-homogeneous space G/H is said to be spherical if H has a finite number of orbits in G/B. A class of spherical homogeneous spaces containing the tori, the complete homogeneous spaces and the group G (viewed as a G × G-homogeneous space) has particularly nice… (More)

- N Ressayre
- 2009

Let G be a connected reductive subgroup of a complex connected reductive groupˆG. Fix maximal tori and Borel subgroups of G andˆG. Consider the cone LR • (ˆ G, G) generated by the pairs (ν, ˆ ν) of strictly dominant characters such that V ν is a submodule of V ˆ ν. The main result of this article is a bijective parametrisation of the faces of LR • (ˆ G, G).… (More)

In [3], Belkale and Kumar define a new product on the cohomology of flag varieties and use this new product to give an improved solution to the eigencone problem for complex reductive groups. In this paper, we give a generalization of the Belkale-Kumar product to the branching Schubert calculus setting. The study of Branching Schubert calculus attempts to… (More)

- N Ressayre
- 2008

1 Introduction

- N Ressayre
- 2009

Let K be a connected compact Lie group. The triples (O 1 , O 2 , O 3) of adjoint K-orbits such that O 1 +O 2 +O 3 contains 0 are parametrized by a closed convex polyhedral cone. This cone is denoted Γ(K) and called the eigencone of K. For K simple of type A, B or C we give an inductive cohomology free description of the minimal set of linear inequalities… (More)