Corrections to the ATLAS of Brauer Characters


This is the list of known errors in the ATLAS of Brauer Characters.
We denote mathematical errors by ***. We use C to denote improvements concerning grammar or notational consistency. Changes are shown in order of appearance.


Introduction


***   p.   xi   :   
Replace the last paragraph of Section 10 by the following.
If the indicator is 0, then D(G) may or may not embed in a suitable unitary group. Let *q be the map on the Brauer characters induced by the field automorphism x → xq. Then D is unitary if and only if D(G) is defined over a field with q2 elements and φ*q is the complex conjugate of φ.


The Tables


***   p.   22   L3(3)   :   
In the 13 modular table, change 12A  12A to 12A  ∗.
***   p.   30-32   L2(25)   :   
Change element orders of 4C, 12C, 12D in 4.G.23 to 4, 12, 12.
***   p.   71-73   U3(4)   :   
Change class names 10A-B in G.2 to 10E-F.
***   p.   79-81   U3(5)   :   
In G.2, change 6C to 6D and 8B to 8C where applicable.
***   p.   108   S4(4)   :   
In G.4, insert fusion signs joining characters 3 and 4, 6 and 7, 9 to 12, 13 and 14.
***   p.   118   L3(7)   :   
Change D∗40 to D∗∗5.
***   p.   130-139   U4(3)   :   
Change class name 12J in G.23 to 12K.
C   p.   170   L4(3)   :   
Swap the two fusion markers for φ27-φ30 in 2.G.21.
C   p.   181   U5(2)   :   
Change chis to phis.
C   p.   186   L3(8)   :   
Rewrite y′63∗∗− z21∗10&17 to y′63∗∗+ z7. (Both expressions are equal.)
***               
In the third and fourth degree 511 rows of the 73 modular table, exchange the indicators °6 and °2 in G.3.
***   p.   204-205   L3(9)   :   
In the 7 modular table of G.21, change the indicator of the second degree 910 character from ++ to ++2. In the 13 modular table of G.23, change the indicator of the second degree 91 character from °° to °°2.
***   p.   206   U3(9)   :   
Change the value of the first degree 584 character on the class 5EF from ∗ to 2+b5∗.
***   p.   219   J3   :   
Swap the character values in G and 3.G on the classes 17A and 17B, and the character values in G.2 on the classes 34A and 34B.


Appendix 1


C   p.   284   :   
Add the entry w41∗3 | X3 + X2 + X | C5.
***   p.   286   :   
The entries for b29 and b29∗ must be as follows. b29 | X + 2 | C2, b29∗| 2 X | C2.
***   p.   288   :   
Replace y9∗∗ by y9∗2.


Appendix 2


C   p.   300   :   
Remove the last change for U3(8), which suggests to add a note to the map. Note that the isoclines of 3.G.31 are in fact isomorphic.


The number of changes of each type is as follows: 14 *** 5 C.

File created on 18 April 2000
Last modified: 17 October 2024 by Thomas Breuer


File translated from TEX by TTH, version 3.59.
On 17 Oct 2024, 22:49.