Why the character of any representation is a central function?Few questions on Character of representation .Character table from a representation?What is the central idempotent of a representation?Character as sum with regular representationCharacter of a RepresentationAdditive character : For any field or for a finite field?Class function and character of $S_3$ representationCharacter regular representationUnitary Central Character by Schur's LemmaWhen is a class function the character of a representation?
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Why the character of any representation is a central function?
Few questions on Character of representation .Character table from a representation?What is the central idempotent of a representation?Character as sum with regular representationCharacter of a RepresentationAdditive character : For any field or for a finite field?Class function and character of $S_3$ representationCharacter regular representationUnitary Central Character by Schur's LemmaWhen is a class function the character of a representation?
$begingroup$
Why the character of any representation is a central function?
Could anyone explain this for me please?
representation-theory characters
asked Mar 29 at 15:31
SmartSmart
827
$endgroup$
add a comment |
$begingroup$
Why the character of any representation is a central function?
Could anyone explain this for me please?
representation-theory characters
asked Mar 29 at 15:31
SmartSmart
827
$endgroup$
1
$begingroup$
Because similar matrices have the same trace. Or are you also looking for an explanation of that (which is a pure linear-algebra fract)?
$endgroup$
– Henning Makholm
Mar 29 at 15:38
add a comment |
$begingroup$
Why the character of any representation is a central function?
Could anyone explain this for me please?
representation-theory characters
asked Mar 29 at 15:31
SmartSmart
827
$endgroup$
Why the character of any representation is a central function?
Could anyone explain this for me please?
representation-theory characters
representation-theory characters
asked Mar 29 at 15:31
SmartSmart
827
asked Mar 29 at 15:31
SmartSmart
827
asked Mar 29 at 15:31
SmartSmart
827
asked Mar 29 at 15:31
SmartSmart
827
asked Mar 29 at 15:31
SmartSmart
827
827
1
$begingroup$
Because similar matrices have the same trace. Or are you also looking for an explanation of that (which is a pure linear-algebra fract)?
$endgroup$
– Henning Makholm
Mar 29 at 15:38
add a comment |
1
$begingroup$
Because similar matrices have the same trace. Or are you also looking for an explanation of that (which is a pure linear-algebra fract)?
$endgroup$
– Henning Makholm
Mar 29 at 15:38
1
1
$begingroup$
Because similar matrices have the same trace. Or are you also looking for an explanation of that (which is a pure linear-algebra fract)?
$endgroup$
– Henning Makholm
Mar 29 at 15:38
$begingroup$
Because similar matrices have the same trace. Or are you also looking for an explanation of that (which is a pure linear-algebra fract)?
$endgroup$
– Henning Makholm
Mar 29 at 15:38
add a comment |
1 Answer
1
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oldest
votes
$begingroup$
Because the character $chi(g)$ is the trace of the action of $g$ and because any two similar matrices have the same trace.
answered Mar 29 at 15:38
José Carlos SantosJosé Carlos Santos
173k23133241
$endgroup$
add a comment |
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$begingroup$
Because the character $chi(g)$ is the trace of the action of $g$ and because any two similar matrices have the same trace.
answered Mar 29 at 15:38
José Carlos SantosJosé Carlos Santos
173k23133241
$endgroup$
add a comment |
$begingroup$
Because the character $chi(g)$ is the trace of the action of $g$ and because any two similar matrices have the same trace.
answered Mar 29 at 15:38
José Carlos SantosJosé Carlos Santos
173k23133241
$endgroup$
add a comment |
$begingroup$
Because the character $chi(g)$ is the trace of the action of $g$ and because any two similar matrices have the same trace.
answered Mar 29 at 15:38
José Carlos SantosJosé Carlos Santos
173k23133241
$endgroup$
Because the character $chi(g)$ is the trace of the action of $g$ and because any two similar matrices have the same trace.
answered Mar 29 at 15:38
José Carlos SantosJosé Carlos Santos
173k23133241
answered Mar 29 at 15:38
José Carlos SantosJosé Carlos Santos
173k23133241
answered Mar 29 at 15:38
José Carlos SantosJosé Carlos Santos
173k23133241
answered Mar 29 at 15:38
José Carlos SantosJosé Carlos Santos
173k23133241
173k23133241
add a comment |
add a comment |
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Because similar matrices have the same trace. Or are you also looking for an explanation of that (which is a pure linear-algebra fract)?
$endgroup$
– Henning Makholm
Mar 29 at 15:38