feat(RepresentationTheory/Character): add integral result for character and conjugacy classes

[Yu-Misaka]

---

• depends on: [Merged by Bors] - feat(RepresentationTheory/Intertwining): a central element of the MonoidAlgebra acts on a representation as self-intertwining map #41400
• depends on: feat(GroupTheory): summation over a conjugacy class #41326

[github-actions]

PR summary d44f8036a4

Import changes exceeding 2%

%	File
+4.43%	Mathlib.Algebra.Group.Conj

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Algebra.Group.Conj	361	377	+16 (+4.43%)

Import changes for all files

Files	Import difference
Mathlib.Algebra.Group.Conj Mathlib.Algebra.GroupWithZero.Conj	16
Mathlib.RepresentationTheory.Canary (new file)	2140

---

Declarations diff (regex)

+ IntertwiningMap.sumConj
+ IntertwiningMap.sumConj.toLinearMap
+ IntertwiningMap.sumConj_apply
+ IntertwiningMap.toLinearMap_one
+ bijOn_conj
+ isIntegral_card_conjClass_smul_char_div_char_one
+ mk_conj
+ prod_carrier_conj
+ prod_carrier_mul_left

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean -- pending)

Computed after the build finishes.

---

No changes to strong technical debt.

Increase in weak tech debt: (relative, absolute) = (1.00, 0.00)

Current number	Change	Type (weak)
5002	1	exposed public sections

Current commit d44f8036a4
Reference commit 92cc40faf5

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[mathlib-dependent-issues]

This PR/issue depends on:

• [Merged by Bors] - feat(RepresentationTheory/Intertwining): a central element of the MonoidAlgebra acts on a representation as self-intertwining map #41400
• feat(GroupTheory): summation over a conjugacy class #41326
  By Dependent Issues (🤖). Happy coding!

[Yu-Misaka]

I'll remove this file before marking the PR as ready for review.