representation_theory.character | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

55b3f820

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

1a51edf1

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2022 Antoine Labelle. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Antoine Labelle
 -/
-import Mathbin.RepresentationTheory.FdRep
-import Mathbin.LinearAlgebra.Trace
-import Mathbin.RepresentationTheory.Invariants
+import RepresentationTheory.FdRep
+import LinearAlgebra.Trace
+import RepresentationTheory.Invariants
 
 #align_import representation_theory.character from "leanprover-community/mathlib"@"1a51edf13debfcbe223fa06b1cb353b9ed9751cc"

1a51edf1

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Antoine Labelle. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Antoine Labelle
-
-! This file was ported from Lean 3 source module representation_theory.character
-! leanprover-community/mathlib commit 1a51edf13debfcbe223fa06b1cb353b9ed9751cc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RepresentationTheory.FdRep
 import Mathbin.LinearAlgebra.Trace
 import Mathbin.RepresentationTheory.Invariants
 
+#align_import representation_theory.character from "leanprover-community/mathlib"@"1a51edf13debfcbe223fa06b1cb353b9ed9751cc"
+
 /-!
 # Characters of representations

1a51edf1

bump to nightly-2023-07-09-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a51edf13debfcbe223fa06b1cb353b9ed9751cc

e0217a15

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Antoine Labelle
 
 ! This file was ported from Lean 3 source module representation_theory.character
-! leanprover-community/mathlib commit 55b3f8206b8596db8bb1804d8a92814a0b6670c9
+! leanprover-community/mathlib commit 1a51edf13debfcbe223fa06b1cb353b9ed9751cc
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.RepresentationTheory.Invariants
 /-!
 # Characters of representations
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file introduces characters of representation and proves basic lemmas about how characters
 behave under various operations on representations.

55b3f820

bump to nightly-2023-07-03-15

mathlib commit https://github.com/leanprover-community/mathlib/commit/9240e8be927a0955b9a82c6c85ef499ee3a626b8

a1e5ab5d

Diff

@@ -40,32 +40,42 @@ section Monoid
 
 variable {G : Type u} [Monoid G]
 
+#print FdRep.character /-
 /-- The character of a representation `V : fdRep k G` is the function associating to `g : G` the
 trace of the linear map `V.ρ g`.-/
 def character (V : FdRep k G) (g : G) :=
   LinearMap.trace k V (V.ρ g)
 #align fdRep.character FdRep.character
+-/
 
+#print FdRep.char_mul_comm /-
 theorem char_mul_comm (V : FdRep k G) (g : G) (h : G) : V.character (h * g) = V.character (g * h) :=
   by simp only [trace_mul_comm, character, map_mul]
 #align fdRep.char_mul_comm FdRep.char_mul_comm
+-/
 
+#print FdRep.char_one /-
 @[simp]
 theorem char_one (V : FdRep k G) : V.character 1 = FiniteDimensional.finrank k V := by
   simp only [character, map_one, trace_one]
 #align fdRep.char_one FdRep.char_one
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print FdRep.char_tensor /-
 /-- The character is multiplicative under the tensor product. -/
 @[simp]
 theorem char_tensor (V W : FdRep k G) : (V ⊗ W).character = V.character * W.character := by ext g;
   convert trace_tensor_product' (V.ρ g) (W.ρ g)
 #align fdRep.char_tensor FdRep.char_tensor
+-/
 
+#print FdRep.char_iso /-
 /-- The character of isomorphic representations is the same. -/
 theorem char_iso {V W : FdRep k G} (i : V ≅ W) : V.character = W.character := by ext g;
   simp only [character, FdRep.Iso.conj_ρ i]; exact (trace_conj' (V.ρ g) _).symm
 #align fdRep.char_iso FdRep.char_iso
+-/
 
 end Monoid
 
@@ -73,29 +83,37 @@ section Group
 
 variable {G : Type u} [Group G]
 
+#print FdRep.char_conj /-
 /-- The character of a representation is constant on conjugacy classes. -/
 @[simp]
 theorem char_conj (V : FdRep k G) (g : G) (h : G) : V.character (h * g * h⁻¹) = V.character g := by
   rw [char_mul_comm, inv_mul_cancel_left]
 #align fdRep.char_conj FdRep.char_conj
+-/
 
+#print FdRep.char_dual /-
 @[simp]
 theorem char_dual (V : FdRep k G) (g : G) : (of (dual V.ρ)).character g = V.character g⁻¹ :=
   trace_transpose' (V.ρ g⁻¹)
 #align fdRep.char_dual FdRep.char_dual
+-/
 
+#print FdRep.char_linHom /-
 @[simp]
 theorem char_linHom (V W : FdRep k G) (g : G) :
     (of (linHom V.ρ W.ρ)).character g = V.character g⁻¹ * W.character g := by
   rw [← char_iso (dual_tensor_iso_lin_hom _ _), char_tensor, Pi.mul_apply, char_dual]
 #align fdRep.char_lin_hom FdRep.char_linHom
+-/
 
 variable [Fintype G] [Invertible (Fintype.card G : k)]
 
+#print FdRep.average_char_eq_finrank_invariants /-
 theorem average_char_eq_finrank_invariants (V : FdRep k G) :
     ⅟ (Fintype.card G : k) • ∑ g : G, V.character g = finrank k (invariants V.ρ) := by
   rw [← (is_proj_average_map V.ρ).trace]; simp [character, GroupAlgebra.average, _root_.map_sum]
 #align fdRep.average_char_eq_finrank_invariants FdRep.average_char_eq_finrank_invariants
+-/
 
 end Group
 
@@ -107,6 +125,7 @@ open scoped Classical
 
 variable [Fintype G] [Invertible (Fintype.card G : k)]
 
+#print FdRep.char_orthonormal /-
 /-- Orthogonality of characters for irreducible representations of finite group over an
 algebraically closed field whose characteristic doesn't divide the order of the group. -/
 theorem char_orthonormal (V W : FdRep k G) [Simple V] [Simple W] :
@@ -130,6 +149,7 @@ theorem char_orthonormal (V W : FdRep k G) [Simple V] [Simple W] :
   -- By Schur's Lemma, the dimension of `Hom_G(W, V)` is `1` is `V ≅ W` and `0` otherwise.
   rw_mod_cast [finrank_hom_simple_simple W V, iso.nonempty_iso_symm]
 #align fdRep.char_orthonormal FdRep.char_orthonormal
+-/
 
 end Orthogonality

55b3f820

bump to nightly-2023-06-10-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

3fdc57bc

Diff

@@ -93,7 +93,7 @@ theorem char_linHom (V W : FdRep k G) (g : G) :
 variable [Fintype G] [Invertible (Fintype.card G : k)]
 
 theorem average_char_eq_finrank_invariants (V : FdRep k G) :
-    (⅟ (Fintype.card G : k) • ∑ g : G, V.character g) = finrank k (invariants V.ρ) := by
+    ⅟ (Fintype.card G : k) • ∑ g : G, V.character g = finrank k (invariants V.ρ) := by
   rw [← (is_proj_average_map V.ρ).trace]; simp [character, GroupAlgebra.average, _root_.map_sum]
 #align fdRep.average_char_eq_finrank_invariants FdRep.average_char_eq_finrank_invariants
 
@@ -110,7 +110,7 @@ variable [Fintype G] [Invertible (Fintype.card G : k)]
 /-- Orthogonality of characters for irreducible representations of finite group over an
 algebraically closed field whose characteristic doesn't divide the order of the group. -/
 theorem char_orthonormal (V W : FdRep k G) [Simple V] [Simple W] :
-    (⅟ (Fintype.card G : k) • ∑ g : G, V.character g * W.character g⁻¹) =
+    ⅟ (Fintype.card G : k) • ∑ g : G, V.character g * W.character g⁻¹ =
       if Nonempty (V ≅ W) then ↑1 else ↑0 :=
   by
   -- First, we can rewrite the summand `V.character g * W.character g⁻¹` as the character

55b3f820

bump to nightly-2023-05-28-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

8d353152

Diff

@@ -30,7 +30,7 @@ universe u
 
 open CategoryTheory LinearMap CategoryTheory.MonoidalCategory Representation FiniteDimensional
 
-open BigOperators
+open scoped BigOperators
 
 variable {k : Type u} [Field k]
 
@@ -103,7 +103,7 @@ section Orthogonality
 
 variable {G : GroupCat.{u}} [IsAlgClosed k]
 
-open Classical
+open scoped Classical
 
 variable [Fintype G] [Invertible (Fintype.card G : k)]

55b3f820

bump to nightly-2023-05-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6797a637

Diff

@@ -58,18 +58,13 @@ theorem char_one (V : FdRep k G) : V.character 1 = FiniteDimensional.finrank k V
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- The character is multiplicative under the tensor product. -/
 @[simp]
-theorem char_tensor (V W : FdRep k G) : (V ⊗ W).character = V.character * W.character :=
-  by
-  ext g
+theorem char_tensor (V W : FdRep k G) : (V ⊗ W).character = V.character * W.character := by ext g;
   convert trace_tensor_product' (V.ρ g) (W.ρ g)
 #align fdRep.char_tensor FdRep.char_tensor
 
 /-- The character of isomorphic representations is the same. -/
-theorem char_iso {V W : FdRep k G} (i : V ≅ W) : V.character = W.character :=
-  by
-  ext g
-  simp only [character, FdRep.Iso.conj_ρ i]
-  exact (trace_conj' (V.ρ g) _).symm
+theorem char_iso {V W : FdRep k G} (i : V ≅ W) : V.character = W.character := by ext g;
+  simp only [character, FdRep.Iso.conj_ρ i]; exact (trace_conj' (V.ρ g) _).symm
 #align fdRep.char_iso FdRep.char_iso
 
 end Monoid
@@ -98,10 +93,8 @@ theorem char_linHom (V W : FdRep k G) (g : G) :
 variable [Fintype G] [Invertible (Fintype.card G : k)]
 
 theorem average_char_eq_finrank_invariants (V : FdRep k G) :
-    (⅟ (Fintype.card G : k) • ∑ g : G, V.character g) = finrank k (invariants V.ρ) :=
-  by
-  rw [← (is_proj_average_map V.ρ).trace]
-  simp [character, GroupAlgebra.average, _root_.map_sum]
+    (⅟ (Fintype.card G : k) • ∑ g : G, V.character g) = finrank k (invariants V.ρ) := by
+  rw [← (is_proj_average_map V.ρ).trace]; simp [character, GroupAlgebra.average, _root_.map_sum]
 #align fdRep.average_char_eq_finrank_invariants FdRep.average_char_eq_finrank_invariants
 
 end Group

55b3f820

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

55b3f820

doc: replace mathlib3 names in doc comments (#11952)

A few miscellaneous directories: RingTheory, SetTheory, Combinatorics and CategoryTheory.

Co-authored-by: Scott Morrison <scott@tqft.net>

de7e5c09

Diff

@@ -41,7 +41,7 @@ open scoped BigOperators
 variable {k : Type u} [Field k]
 
 namespace FdRep
-set_option linter.uppercaseLean3 false -- `fdRep`
+set_option linter.uppercaseLean3 false -- `FdRep`
 
 section Monoid

55b3f820

doc(RepresentationTheory): add some doc for three basic files (#11643)

Add some doc concerning Schur's lemma, orthogonality of characters and irreducible representations being defined as simple objects.

7f145201

Diff

@@ -15,6 +15,15 @@ import Mathlib.RepresentationTheory.Invariants
 This file introduces characters of representation and proves basic lemmas about how characters
 behave under various operations on representations.
 
+A key result is the orthogonality of characters for irreducible representations of finite group
+over an algebraically closed field whose characteristic doesn't divide the order of the group. It
+is the theorem `char_orthonormal`
+
+# Implementation notes
+
+Irreducible representations are implemented categorically, using the `Simple` class defined in
+`Mathlib.CategoryTheory.Simple`
+
 # TODO
 * Once we have the monoidal closed structure on `FdRep k G` and a better API for the rigid
 structure, `char_dual` and `char_linHom` should probably be stated in terms of `Vᘁ` and `ihom V W`.

55b3f820

chore: only four spaces for subsequent lines (#7286)

Co-authored-by: Moritz Firsching <firsching@google.com>

0c7d6fa5

Diff

@@ -61,7 +61,7 @@ theorem char_tensor (V W : FdRep k G) : (V ⊗ W).character = V.character * W.ch
 -- Porting note: adding variant of `char_tensor` to make the simp-set confluent
 @[simp]
 theorem char_tensor' (V W : FdRep k G) :
-  character (Action.FunctorCategoryEquivalence.inverse.obj
+    character (Action.FunctorCategoryEquivalence.inverse.obj
     (Action.FunctorCategoryEquivalence.functor.obj V ⊗
      Action.FunctorCategoryEquivalence.functor.obj W)) = V.character * W.character := by
   simp [← char_tensor]

55b3f820

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Antoine Labelle. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Antoine Labelle
-
-! This file was ported from Lean 3 source module representation_theory.character
-! leanprover-community/mathlib commit 55b3f8206b8596db8bb1804d8a92814a0b6670c9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RepresentationTheory.FdRep
 import Mathlib.LinearAlgebra.Trace
 import Mathlib.RepresentationTheory.Invariants
 
+#align_import representation_theory.character from "leanprover-community/mathlib"@"55b3f8206b8596db8bb1804d8a92814a0b6670c9"
+
 /-!
 # Characters of representations

55b3f820

feat: port RepresentationTheory.Character (#5679)

Co-authored-by: Johan Commelin <johan@commelin.net>

9c8d5b1c

`representation_theory.character` ⟷ `Mathlib.RepresentationTheory.Character`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 11 + 883

representation_theory.character ⟷ Mathlib.RepresentationTheory.Character

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 11 + 883

`representation_theory.character` ⟷ `Mathlib.RepresentationTheory.Character`