Question

Showing that $\sum_{\rho}\chi_\rho(g)\overline{\chi_\rho(g)} = \frac{|G|}{|C(g)|}$ for a finite group $G$, $g \in G$ and $C(g)$ a conjugacy class

score 135 · Answer 1 · 2022-04-09 12:30:41

135

Views

Showing that $\sum_{\rho}\chi_\rho(g)\overline{\chi_\rho(g)} = \frac{|G|}{|C(g)|}$ for a finite group $G$, $g \in G$ and $C(g)$ a conjugacy class

Published on 09 Apr 2022 - 12:30

score 87 · Answer 2 · 2022-04-09 15:23:43

87

Views

Intuitions behind Frobenius' generalization of characters to nonabelian finite group given the historical context

Published on 09 Apr 2022 - 15:23

score 53 · Answer 3 · 2022-04-10 07:53:09

53

Views

Showing that if a class function $\gamma$ is orthogonal to all irreducible representations of a finite group $G$ then $\gamma \equiv 0$.

Published on 10 Apr 2022 - 7:53

score 37 · Answer 4 · 2026-02-28 00:03:19

37

Views

Characters of irreducible representations of a finite and semisimple algebra

Published on 28 Feb 2026 - 0:03

score 99 · Answer 5 · 2022-04-17 01:53:53

99

Views

Direct sum decomposition of $\mathbb CG$ module into simple modules given the character table of $G$ (regular representation)

Published on 17 Apr 2022 - 1:53

score 53 · Answer 6 · 2022-04-21 10:21:33

53

Views

Relation between characters and coordinate ring

Published on 21 Apr 2022 - 10:21

score 204 · Answer 7 · 2026-03-26 01:17:55

204

Views

Computing $\chi(1)$ and $\chi(s)$ for $\chi\in\widehat{\mathrm{GL}_2(\mathbb{F}_q)}$ and semisimple non-regular $s$ using formulas of Deligne-Lusztig

Published on 26 Mar 2026 - 1:17

score 64 · Answer 8 · 2022-04-23 20:29:04

64

Views

Extension in semidirect case

Published on 23 Apr 2022 - 20:29

score 49 · Answer 9 · 2022-04-24 14:16:51

49

Views

Method Verification for Finding Irreducible Characters

Published on 24 Apr 2022 - 14:16

score 419 · Answer 10 · 2026-03-29 03:21:48

419

Views

Determine if a group is simple from character table

Published on 29 Mar 2026 - 3:21

score 107 · Answer 11 · 2022-04-30 17:41:30

107

Views

Induced representation coefficients

Published on 30 Apr 2022 - 17:41

score 256 · Answer 12 · 2022-05-11 05:04:25

256

Views

Application of character theory to structure of groups

Published on 11 May 2022 - 5:04

score 69 · Answer 13 · 2022-05-11 18:58:27

If $G$ is a finite group, $g \in G$, and $\chi$ is a character of $G$, what are the definitions of "$\chi(g)$" and "$\overline{\chi(g)}$"?

score 61 · Answer 14 · 2022-05-21 17:08:11

61

Views

Positive column in the character table of finite groups

Published on 21 May 2022 - 17:08

score 86 · Answer 15 · 2022-05-22 15:18:24

86

Views

Induced rep of restriction of irreducible rep

Published on 22 May 2022 - 15:18

List Question

Showing that $\sum_{\rho}\chi_\rho(g)\overline{\chi_\rho(g)} = \frac{|G|}{|C(g)|}$ for a finite group $G$, $g \in G$ and $C(g)$ a conjugacy class

Intuitions behind Frobenius' generalization of characters to nonabelian finite group given the historical context

Showing that if a class function $\gamma$ is orthogonal to all irreducible representations of a finite group $G$ then $\gamma \equiv 0$.

Characters of irreducible representations of a finite and semisimple algebra

Direct sum decomposition of $\mathbb CG$ module into simple modules given the character table of $G$ (regular representation)

Relation between characters and coordinate ring

Computing $\chi(1)$ and $\chi(s)$ for $\chi\in\widehat{\mathrm{GL}_2(\mathbb{F}_q)}$ and semisimple non-regular $s$ using formulas of Deligne-Lusztig

Extension in semidirect case

Method Verification for Finding Irreducible Characters

Determine if a group is simple from character table

Induced representation coefficients

Application of character theory to structure of groups

If $G$ is a finite group, $g \in G$, and $\chi$ is a character of $G$, what are the definitions of "$\chi(g)$" and "$\overline{\chi(g)}$"?

Positive column in the character table of finite groups

Induced rep of restriction of irreducible rep

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