52,916 research outputs found
Effective Invariant Theory of Permutation Groups using Representation Theory
Using the theory of representations of the symmetric group, we propose an
algorithm to compute the invariant ring of a permutation group. Our approach
have the goal to reduce the amount of linear algebra computations and exploit a
thinner combinatorial description of the invariant ring.Comment: Draft version, the corrected full version is available at
http://www.springer.com
A subexponential-time quantum algorithm for the dihedral hidden subgroup problem
We present a quantum algorithm for the dihedral hidden subgroup problem with
time and query complexity . In this problem an oracle
computes a function on the dihedral group which is invariant under a
hidden reflection in . By contrast the classical query complexity of DHSP
is . The algorithm also applies to the hidden shift problem for an
arbitrary finitely generated abelian group.
The algorithm begins with the quantum character transform on the group, just
as for other hidden subgroup problems. Then it tensors irreducible
representations of and extracts summands to obtain target
representations. Finally, state tomography on the target representations
reveals the hidden subgroup.Comment: 11 pages. Revised in response to referee reports. Early sections are
more accessible; expanded section on other hidden subgroup problem
Group theory factors for Feynman diagrams
We present algorithms for the group independent reduction of group theory
factors of Feynman diagrams. We also give formulas and values for a large
number of group invariants in which the group theory factors are expressed.
This includes formulas for various contractions of symmetric invariant tensors,
formulas and algorithms for the computation of characters and generalized
Dynkin indices and trace identities. Tables of all Dynkin indices for all
exceptional algebras are presented, as well as all trace identities to order
equal to the dual Coxeter number. Further results are available through
efficient computer algorithms (see http://norma.nikhef.nl/~t58/ and
http://norma.nikhef.nl/~t68/ ).Comment: Latex (using axodraw.sty), 47 page
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