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{
"version": "Oct 17, 2024",
"description": "the contents of the list of Improvements to the ATLAS of Brauer Characters",
"data": [
{
"section": "Introduction",
"entries": [
[ "***", "p. xi", "", "Replace the last paragraph of Section 10 by the following.<<nl>>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 $x \\mapsto x^q$. Then $D$ is unitary if and only if $D(G)$ is defined over a field with $q^2$ elements and $\\varphi^{*q}$ is the complex conjugate of $\\varphi$.", "I" ]
]
},
{
"section": "The Tables",
"entries": [
[ "***", "p. 22", "L_3(3)", "In the $13$ modular table, change $12A 12A$ to $12A \\ast$.", "P" ],
[ "***", "p. 30--32", "L_2(25)", "Change element orders of $4C$, $12C$, $12D$ in $4.G.2_3$ to $4$, $12$, $12$.", "P" ],
[ "***", "p. 71--73", "U_3(4)", "Change class names $10A$--$B$ in $G.2$ to $10E$--$F$.", "P" ],
[ "***", "p. 79--81", "U_3(5)", "In $G.2$, change $6C$ to $6D$ and $8B$ to $8C$ where applicable.", "P" ],
[ "***", "p. 108", "S_4(4)", "In $G.4$, insert fusion signs joining characters 3 and 4, 6 and 7, 9 to 12, 13 and 14.", "FI" ],
[ "***", "p. 118", "L_3(7)", "Change $D\\ast 40$ to $D\\ast\\ast 5$.", "P" ],
[ "***", "p. 130--139", "U_4(3)", "Change class name $12J$ in $G.2_3$ to $12K$.", "P" ],
[ "C", "p. 170", "L_4(3)", "Swap the two fusion markers for $\\varphi_{27}$--$\\varphi_{30}$ in $2.G.2_1$." ],
[ "C", "p. 181", "U_5(2)", "Change chis to phis." ],
[ "C", "p. 186", "L_3(8)", "Rewrite $y'63\\ast\\ast - z21\\ast 10\\&17$ to $y'63\\ast\\ast + z7$. (Both expressions are equal.)" ],
[ "***", "p. 186", "L_3(8)", "In the third and fourth degree $511$ rows of the $73$ modular table, exchange the indicators ${\\circ}6$ and ${\\circ}2$ in $G.3$.", "FI" ],
[ "***", "p. 204--205", "L_3(9)", "In the 7 modular table of $G.2_1$, change the indicator of the second degree 910 character from ${+}{+}$ to ${+}{+}2$. In the 13 modular table of $G.2_3$, change the indicator of the second degree 91 character from ${\\circ}{\\circ}$ to ${\\circ}{\\circ}2$.", "FI" ],
[ "***", "p. 206", "U_3(9)", "Change the value of the first degree 584 character on the class $5EF$ from $\\ast$ to $2+b5\\ast$.", "CH" ],
[ "***", "p. 219", "J_3", "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 $34B$.", "CH" ]
]
},
{
"section": "Appendix 1",
"entries": [
[ "C", "p. 284", "", "Add the entry $w41\\ast 3 | X^3 + X^2 + X | C_5$." ],
[ "***", "p. 286", "", "The entries for $b29$ and $b29\\ast$ must be as follows. $b29 | X + 2 | C_2$, $b29\\ast | 2 X | C_2$.", "I" ],
[ "***", "p. 288", "", "Replace $y9\\ast\\ast$ by $y9\\ast2$.", "I" ]
]
},
{
"section": "Appendix 2",
"entries": [
[ "C", "p. 300", "", "Remove the last change for $U_3(8)$, which suggests to add a note to the map. Note that the isoclines of $3.G.3_1$ are in fact isomorphic." ]
]
}
]
}
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