منابع مشابه
Fundamental invariants of orbit closures
For several objects of interest in geometric complexity theory, namely for the determinant, the permanent, the product of variables, the power sum, the unit tensor, and the matrix multiplication tensor, we introduce and study a fundamental SL-invariant function that relates the coordinate ring of the orbit with the coordinate ring of its closure. For the power sums we can write down this fundam...
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We give new classes of examples of orbits of the diagonal group in the space of unit volume lattices in R for d ≥ 3 with nice (homogeneous) orbit closures, as well as examples of orbits with explicitly computable but irregular orbit closures. We give Diophantine applications to the former, for instance we show that for all γ, δ ∈ R lim inf |n|→∞ |n| 〈n 3 √ 2− γ〉〈n 3 √ 4− δ〉 = 0, where 〈c〉 denot...
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This is an expository article on the singularities of nilpotent orbit closures in simple Lie algebras over the complex numbers. It is slanted towards aspects that are relevant for representation theory, including Ma ei's theorem relating Slodowy slices to Nakajima quiver varieties in type A. There is one new observation: the results of Juteau and Mautner, combined with Ma ei's theorem, give a g...
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Equivalence of matrix pencils (pairs of pq matrices over C) is given by the GL p GL q-action of simultaneous left and right multiplication. The orbits under this group action were described by Kronecker in 1890 in terms of pencil invariants: column indices, row indices, and elementary divisors. In this paper we describe the topological closures of these orbits, a problem motivated by our work i...
متن کاملOrbit Closures in the Enhanced Nilpotent Cone
We study the orbits of G = GL(V ) in the enhanced nilpotent cone V ×N , where N is the variety of nilpotent endomorphisms of V . These orbits are parametrized by bipartitions of n = dimV , and we prove that the closure ordering corresponds to a natural partial order on bipartitions. Moreover, we prove that the local intersection cohomology of the orbit closures is given by certain bipartition a...
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2019
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-019-02228-6