Atlas of Lie Groups and Representations

Documentation contents

Script File

test_unitarity.at

test list [(Param p,bool answer)],
test p for unitarity and compare result with answer
prints:
  parameter,
  computed unitarity,
  claimed unitarity,
  number of reducibility points,
  number of deformations
Source
atlas-scripts/test_unitarity.at (185 lines)
Definitions
23
Loads
Loaded by
none of the other all.at files

Definitions in source order

uflag 2 overloads

L18uflag (int predicted) = string
L21uflag (bool flag) = string

as_predicted

L23as_predicted (int predicted, bool unitary) = bool

passedflag 2 overloads

L25passedflag(int predicted, bool unitary) = string
L27passedflag (bool flag) = string

test 2 overloads

L34test ([(Param,int)] parameters,bool verbose) = (bool,[(Param,KTypePol,int,bool)])
test list of parameters for same group for unitarity/non-unitarity
parameters=[(param p, int predicted)]
predicted takes values 1,0, or -1 which respectively mean
parameter is predicted to be unitary / no prediction / predicted non-unitary
L65test ([(Param,int)] parameters)
default quiet

also in this file at line 70; also defined in all_finite_order.at, nilpotent_centralizer.at, sommers.at

test

L70test([Param] parameters) = (bool,[(Param,KTypePol,int,bool)])

also in this file at line 34, line 65; also defined in all_finite_order.at, nilpotent_centralizer.at, sommers.at

print_test

L72print_test([Param] parameters) = void

also in this file at line 67

test_one

L74test_one (Param param,int unitary) = (bool,[(Param,KTypePol,int,bool)])

test_one_unitary

L78test_one_unitary (Param param) = (bool,[(Param,KTypePol,int,bool)])

test_spherical_unipotent

L85test_spherical_unipotent (RealForm G) = (bool,[(Param,KTypePol,int,bool)])
G should be absolutely simple, SL(n,R), Sp(2n,R), S(n,n) or SO(n+1,n) or
simple complex, see spherical_unipotent_representations in representations.at

test_Aq

L91test_Aq ([Param] B) = (bool,[(Param,KTypePol,int,bool)])

also in this file at line 132

test_Aq

L132test_Aq (RealForm G) = (bool,[(Param,KTypePol,int,bool)])

also in this file at line 91

print_test_Aq

L136print_test_Aq (RealForm G) = void

also in this file at line 104

test_all_real_induced_one_dimensional

L141test_all_real_induced_one_dimensional(RealForm G) = (bool,[(Param,KTypePol,int,bool)])
Commented-out code, lines 147–185 (38 lines)
comment out fixed case tests, though maybe useful for atlas sanity testing

{ a series of tests if increasing length }
{ very fast tests }
set unitary_if (bool b) = int: if b then 1 else -1 fi
set success ((bool,[Param,KTypePol,int,bool]) (b,)) = bool: b

set test1()=test(spherical_unipotent_representations(Sp(4,R))).success
set test2()=test(spherical_unipotent_representations(split_form(G2))).success
set test3()=test(spherical_unipotent_representations(Sp(6,R))).success
set test4()=
  let G2=quasisplit_form(inner_class(adjoint("G2"),"e"))
  then p=trivial(G2) then (B,t)=block(p)
  in test (for p@i in B do (p,unitary_if(i<5 or i=t)) od,true).success

{ slightly longer, up to a few minutes }
set test5()= test(spherical_unipotent_representations (SO(5,4))).success
set test6()=
  let p=trivial(Sp(4,R)) then (B,t)=block(p) in
  test(for p@i in B do (p,unitary_if(i<7 or i=t)) od,true).success

{ first 49 of 59 spherical unitary parameters for F4 }
set test7()= bool:
  test(for i:49
       do minimal_spherical_principal_series
            (split_form(F4),F4_spherical_unitary[i])
       od).success

{ first 100 of spherical unitary for E7
  requires more memory}
set test8()= bool:
  test(for i:100
  do minimal_spherical_principal_series(split_form(E7),E7_spherical_unitary[i])
  od).success

{ trivial of F4 takes up to two hours }
set test9()=bool:
  prints("Testing trivial of F4"); is_unitary(trivial(split_form(F4)))

Generated from atlas-scripts at commit 7e1b958 (2026-09-17).