28 lines
953 B
Julia
28 lines
953 B
Julia
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## Particular definitions for actions on Sp(n,ℤ)
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function _conj(
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t::MatrixGroups.ElementarySymplectic{N,T},
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σ::PermutationGroups.AbstractPerm,
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) where {N,T}
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@assert iseven(N)
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@assert degree(σ) == N ÷ 2 "Got degree = $(degree(σ)); N = $N"
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i = mod1(t.i, N ÷ 2)
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ib = i == t.i ? 0 : N ÷ 2
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j = mod1(t.j, N ÷ 2)
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jb = j == t.j ? 0 : N ÷ 2
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return MatrixGroups.ElementarySymplectic{N}(t.symbol, i^inv(σ) + ib, j^inv(σ) + jb, t.val)
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end
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function _conj(
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t::MatrixGroups.ElementarySymplectic{N,T},
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x::Groups.Constructions.DirectPowerElement,
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) where {N,T}
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@assert Groups.order(Int, parent(x).group) == 2
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@assert iseven(N)
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just_one_flips = xor(isone(x.elts[mod1(t.i, N ÷ 2)]), isone(x.elts[mod1(t.j, N ÷ 2)]))
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return ifelse(just_one_flips, inv(t), t)
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end
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action_by_conjugation(sln::Groups.MatrixGroups.SymplecticGroup, Σ::Groups.Group) =
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AlphabetPermutation(alphabet(sln), Σ, _conj)
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