Mulmuley's efficient generators conjecture for invariant rings
Mulmuley's efficient generators conjecture for invariant rings
Let be a sequence of representations, with an -representation of dimension . An arithmetic circuit succinctly encodes the generators of the invariant ring of an -representation if, after assigning arbitrary complex values to its auxiliary variables, the resulting polynomials are invariants generating as a ring. Then there exists a polynomial and a sequence of arithmetic circuits of size such that succinctly encodes the generators of the invariant ring of . This conjecture asks for uniformly efficient descriptions of generators for invariant rings, a problem motivated by computational complexity and geometric complexity theory. The source states that the original conjecture for remained open, and that Oliveira stated its resolution as an open problem in December 2019.
Sources & referencesView supporting material
Primary source
Christian Ikenmeyer and Michael Walter, “Hyperpfaffians and Geometric Complexity Theory”, arXiv:1912.09389 (2020).
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