From e39c8ea995e4b2b43b57d95cb7700b5b95890b8c Mon Sep 17 00:00:00 2001
From: ThomasBreuer <sam@math.rwth-aachen.de>
Date: Sun, 13 Feb 2022 19:22:26 +0100
Subject: [PATCH] admit `g^chi` and `chi^g` for Brauer characters

---
 lib/ctblfuns.gi              | 53 ++++++++++++++++++++++++++++--------
 tst/testinstall/ctblfuns.tst | 20 +++++++++++++-
 2 files changed, 61 insertions(+), 12 deletions(-)

diff --git a/lib/ctblfuns.gi b/lib/ctblfuns.gi
index 3b4e45a3f4..4ff7e9ba51 100644
--- a/lib/ctblfuns.gi
+++ b/lib/ctblfuns.gi
@@ -521,15 +521,32 @@ InstallMethod( \^,
     "for class function and group element",
     [ IsClassFunction, IsMultiplicativeElementWithInverse ],
     function( chi, g )
-    local tbl, G;
+    local tbl, G, mtbl, pi, fus, inv, imgs;
+
     tbl:= UnderlyingCharacterTable( chi );
     if HasUnderlyingGroup( tbl ) then
+      # 'chi' is an ordinary character.
       G:= UnderlyingGroup( tbl );
       if IsElmsColls( FamilyObj( g ), FamilyObj( G ) ) then
         return ClassFunctionSameType( tbl, chi,
                Permuted( ValuesOfClassFunction( chi ),
                          CorrespondingPermutations( tbl, chi, [ g ] )[1] ) );
       fi;
+    elif HasOrdinaryCharacterTable( tbl ) then
+      # 'chi' is a Brauer character.
+      mtbl:= tbl;
+      tbl:= OrdinaryCharacterTable( mtbl );
+      if HasUnderlyingGroup( tbl ) then
+        G:= UnderlyingGroup( tbl );
+        if IsElmsColls( FamilyObj( g ), FamilyObj( G ) ) then
+          pi:= CorrespondingPermutations( tbl, [ g ] )[1]^-1;
+          fus:= GetFusionMap( mtbl, tbl );
+          inv:= InverseMap( fus );
+          imgs:= List( [ 1 .. Length( fus ) ], i -> inv[ fus[i]^pi ] );
+          return ClassFunctionSameType( mtbl, chi,
+                 ValuesOfClassFunction( chi ){ imgs } );
+        fi;
+      fi;
     fi;
     TryNextMethod();
     end );
@@ -579,20 +596,34 @@ InstallOtherMethod( \^,
 InstallOtherMethod( \^,
     [ IsMultiplicativeElementWithInverse, IsClassFunction ],
     function( g, chi )
-    local tbl, ccl, i;
+    local tbl, mtbl, ccl, i;
+
     tbl:= UnderlyingCharacterTable( chi );
-    if not HasUnderlyingGroup( tbl ) then
+    if HasOrdinaryCharacterTable( tbl ) then
+      # 'chi' is a Brauer character.
+      mtbl:= tbl;
+      tbl:= OrdinaryCharacterTable( mtbl );
+      if not HasUnderlyingGroup( tbl ) then
+        Error( "table <tbl> of <chi> does not store its group" );
+      elif not g in UnderlyingGroup( tbl )
+           or Order( g ) mod UnderlyingCharacteristic( mtbl ) = 0 then
+        Error( "<g> must be p-regular and lie in the underlying group of <chi>" );
+      else
+        ccl:= ConjugacyClasses( tbl ){ GetFusionMap( mtbl, tbl ) };
+      fi;
+    elif not HasUnderlyingGroup( tbl ) then
       Error( "table <tbl> of <chi> does not store its group" );
-    elif g in UnderlyingGroup( tbl ) then
-      ccl:= ConjugacyClasses( tbl );
-      for i in [ 1 .. Length( ccl ) ] do
-        if g in ccl[i] then
-          return ValuesOfClassFunction( chi )[i];
-        fi;
-      od;
-    else
+    elif not g in UnderlyingGroup( tbl ) then
       Error( "<g> must lie in the underlying group of <chi>" );
+    else
+      ccl:= ConjugacyClasses( tbl );
     fi;
+
+    for i in [ 1 .. Length( ccl ) ] do
+      if g in ccl[i] then
+        return ValuesOfClassFunction( chi )[i];
+      fi;
+    od;
     end );
 
 
diff --git a/tst/testinstall/ctblfuns.tst b/tst/testinstall/ctblfuns.tst
index 375db47446..2f64bd89fa 100644
--- a/tst/testinstall/ctblfuns.tst
+++ b/tst/testinstall/ctblfuns.tst
@@ -1,4 +1,4 @@
-#@local S4,V4,irr,l, tbl, v
+#@local S4,V4,irr,l, tbl, v, g, h, t, chi, t5, irr5
 gap> START_TEST("ctblfuns.tst");
 gap> S4:= SymmetricGroup( 4 );
 Sym( [ 1 .. 4 ] )
@@ -67,5 +67,23 @@ fail
 gap> SizeOfFieldOfDefinition( Z(25), 5 );
 Error, <val> must be a cyclotomic or a list of cyclotomics
 
+#
+gap> S4:= SymmetricGroup( 4 );;
+gap> V4:= PCore( S4, 2 );;
+gap> t:= CharacterTable( V4 );;
+gap> irr:= Irr( t );;
+gap> List( irr, chi -> Position( irr, chi^S4.1 ) );
+[ 1, 3, 2, 4 ]
+gap> chi:= irr[2];;
+gap> chi = List( ConjugacyClasses( V4 ), x -> Representative(x)^chi );
+true
+gap> t5:= t mod 5;;
+gap> irr5:= Irr( t5 );;
+gap> List( irr5, chi -> Position( irr5, chi^S4.1 ) );
+[ 1, 3, 2, 4 ]
+gap> chi:= irr5[2];;
+gap> chi = List( ConjugacyClasses( V4 ), x -> Representative(x)^chi );
+true
+
 #
 gap> STOP_TEST( "ctblfuns.tst", 1);