Atlas of Brauer Characters -- Corrections

# 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.