Square death at the super level #
The kill chain: vanishing under the skein representation
propagates through the fibre functor to the conjugated super
permutation action, and in particular the square block idempotent
at any side s > 2eR dies at the super level — the unconditional
half of the sector dichotomy.
theorem
RS.skeinRep_zero_imp_superPermAction_zero
{R : ℕ}
(f : EdgeRankParameter R)
(P : DelignePackage (SkeinObj f))
(n : ℕ)
(x : SymGroupAlgebra n)
(hx : (skeinRep f n) x = 0)
:
The kill chain: vanishing under the skein representation propagates to the super permutation action.
theorem
RS.superPermAction_square_dead
{R : ℕ}
(f : EdgeRankParameter R)
(P : DelignePackage (SkeinObj f))
{s : ℕ}
(hs : 2 * Real.exp 1 * ↑R < ↑s)
:
(superPermAction f P (squareDiagram s).card)
(charIdempotent (nDim (jtSimple (squareDiagram s))) (jtChar (squareDiagram s))) = 0
Square death at the super level: at any side s > 2eR the
super permutation action kills the square block idempotent.