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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)
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)
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)
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)
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)