atlas Library · Script File

`coherent.at`

computing coherent continuations

Source

atlas-scripts/coherent.at (91 lines)

Definitions

Loads

<basic.at
<translate.at { for translation functor T@(Param(Pol),ratvec) }
<kl.at { for |composition_series| }

Loaded by

coherent_irreducible.at induction.at

Definitions in source order

Cayleys as sums of one or two terms L8

`Cayley_sum`

L11Cayley_sum (int k,Param p) = ParamPol

Cayley transform as a sum of one or two terms

coherent continuation in basis of standards L15

DANGEROUS BEND
all versions of coherent continuation action are right actions
   (u*w).p = w*(u*p)
therefore the reflection arguments are written to the right
   coherent_std_reg(p,w*u)=coherent_std_reg(coherent_std_reg(p,w),u)
this ultimately comes down to the inverse on pages 460-461
of Vogan's big green book

L17

coherent continuation action of integrally simple root |s| on Param |p|
in basis of standards; |s| is simple index in the *integrality* root datum

L26

`coherent_std` 7 overloads

L29coherent_std (Param p,int s) = ParamPol

L41coherent_std (ParamPol P,int s) = ParamPol

coherent continuation action of simple root on ParamPol in basis of standards
regular case

L49coherent_std (Param p,[int] w) = ParamPol

coherent continuation action of Weyl group on Param in basis of standards
see the dangerous bend above; this applies [a1,a2,...,an] in
the order ( . * a1 * a2 * ... * an )
this applies to all other invocations of coherent_*

L52coherent_std (Param p,WeylElt w) = ParamPol

L55coherent_std (ParamPol P,[int] w) = ParamPol

coherent continuation action of Weyl group on ParamPol, basis of standards

L60coherent_std (WeylElt v,Param p) = ParamPol

arguments in other order gives the same action:

L61coherent_std (WeylElt v,ParamPol P) = ParamPol

coherent continuation in basis of irreducibles L63

`coherent_irr` 6 overloads

L66coherent_irr (Param p,int s)

coherent continuation of simple root on Param in basis of irreducibles

L70coherent_irr (Param p,[int] w)

coherent continuation of Weyl group element on Param, basis of irreducibles

L72coherent_irr (Param p,WeylElt w) = ParamPol

L75coherent_irr (ParamPol P,int s) = ParamPol

coherent continuation of simple root on ParamPol, basis of irreducibles

L80coherent_irr (ParamPol P,[int] w) = ParamPol

coherent continuation of Weyl group element on ParamPol in
basis of irreducibles

L82coherent_irr (ParamPol P,WeylElt w) = ParamPol

also defined in coherent_irreducible.at

coherent families L84

`coherent_family_irr`

L86coherent_family_irr (ParamPol P, ratvec gamma_target) = ParamPol

Generated from atlas-scripts at commit 648506c (2026-10-13).

coherent.at