User Michael_1812

6 votes

2 answers

341 views

A theorem from the theory of groups

group-theory

asked Nov 28, 2014 at 20:41

6 votes

2 answers

427 views

Dixmier's lemma as a generalisation of Schur's first lemma

asked Jul 19, 2019 at 0:09

5 votes

2 answers

88 views

Simple formulae for matrices

linear-algebra

asked Dec 24, 2017 at 18:20

5 votes

1 answer

72 views

Definition of an Induced Representation. Technicalities.

group-theory representation-theory definition lie-groups

asked May 24, 2020 at 22:25

5 votes

0 answers

62 views

Dot product of functions on cosets

measure-theory harmonic-analysis fiber-bundles principal-bundles haar-measure

asked Jan 31, 2021 at 3:12

5 votes

1 answer

61 views

Two definitions of representation of a topological group

abstract-algebra group-theory representation-theory topological-groups

asked Mar 1, 2021 at 0:54

5 votes

1 answer

87 views

Complete reducibility, in linear algebra versus topology. The example of the translation representation of $\mathbb R$ in $L^2({\mathbb{R}})$

general-topology fourier-analysis representation-theory fast-fourier-transform

asked Oct 10, 2021 at 23:04

4 votes

1 answer

89 views

Quotient representation, in linear algebra and in topology

general-topology representation-theory quotient-spaces

asked Sep 18, 2021 at 19:32

4 votes

1 answer

60 views

Semisimplicity of a group representation

linear-algebra group-theory representation-theory lie-groups

asked Jan 30 at 3:16

4 votes

0 answers

52 views

A simple question on groups and quotient spaces.

group-theory

asked Nov 22, 2018 at 2:32

4 votes

0 answers

118 views

A representation induced from one subgroup and restricted to another

group-theory representation-theory lie-groups

asked Oct 16, 2019 at 18:47

4 votes

1 answer

66 views

A morphism intertwining two induced representations

group-theory lie-groups

asked Oct 31, 2019 at 0:39

3 votes

1 answer

74 views

Morphisms of two fully reducible representations of a group

group-theory representation-theory lie-groups

asked Apr 9, 2020 at 2:39

3 votes

0 answers

197 views

Special functions, Fourier series

fourier-analysis special-functions bessel-functions

asked Nov 9, 2014 at 22:24

3 votes

0 answers

501 views

Restriction of an Induced Representation

group-theory finite-groups representation-theory lie-groups

asked May 11, 2020 at 4:05

3 votes

0 answers

45 views

The Hausdorffness of a locally compact topological group

general-topology topological-groups

asked Jan 19, 2021 at 16:18

3 votes

0 answers

69 views

Functions on a group. Functions of the inverse element.

group-theory measure-theory lie-groups

asked Sep 18, 2020 at 2:10

3 votes

1 answer

172 views

Two definitions of complete algebraic reducibility are equivalent by Zorn's lemma. Does this equivalence stay for topological spaces?

functional-analysis representation-theory harmonic-analysis topological-groups topological-vector-spaces

asked Dec 24, 2021 at 2:15

3 votes

1 answer

92 views

Continuity in topology. An example from Nakahara's book

calculus general-topology geometric-topology

asked Jun 26 at 20:51

2 votes

0 answers

67 views

Splitting of a topological vector space (TVS) into an uncountable number of subspaces

functional-analysis representation-theory harmonic-analysis topological-groups

asked Feb 2 at 2:46

2 votes

0 answers

51 views

On the definition of Banach space

general-topology banach-spaces

asked Sep 19, 2021 at 23:23

2 votes

0 answers

63 views

Complete reducibility, in linear algebra and in topology

general-topology group-theory representation-theory hilbert-spaces

asked Sep 26, 2021 at 7:05

2 votes

1 answer

38 views

On the definition of local compactness

general-topology compactness

asked Nov 24, 2021 at 18:33

2 votes

1 answer

64 views

A topological detail in the definition of Lie group

general-topology lie-groups topological-groups

asked Sep 19, 2020 at 1:17

2 votes

2 answers

60 views

Topological space, manifold, open sets

general-topology manifolds

asked Oct 17, 2020 at 6:35

2 votes

3 answers

188 views

Is a Radon measure always positive on non-empty open sets? The same question about the Haar measure.

measure-theory borel-measures

asked Jan 17, 2021 at 2:41

2 votes

1 answer

39 views

Functions mapping a group to a Hilbert space.

group-theory representation-theory hilbert-spaces

asked Jun 16, 2020 at 1:32

2 votes

0 answers

56 views

Induced representations built on sections of an associated vector bundle. Questions on notations

representation-theory vector-bundles fiber-bundles functors equivariant-maps

asked Feb 28, 2021 at 1:19

2 votes

1 answer

265 views

A detail in the proof of Schur's lemma: the closures of the $\ker$ and $\operatorname{img}$ of the intertwiner.

group-theory representation-theory lie-groups mathematical-physics unbounded-operators

asked May 12, 2021 at 20:04

2 votes

0 answers

72 views

Complement to a subspace, in linear algebra, in topology, in functional analysis

linear-algebra general-topology hilbert-spaces banach-spaces

asked Sep 8, 2021 at 22:21

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47 Questions

A theorem from the theory of groups

Dixmier's lemma as a generalisation of Schur's first lemma

Simple formulae for matrices

Definition of an Induced Representation. Technicalities.

Dot product of functions on cosets

Two definitions of representation of a topological group

Complete reducibility, in linear algebra versus topology. The example of the translation representation of $\mathbb R$ in $L^2({\mathbb{R}})$

Quotient representation, in linear algebra and in topology

Semisimplicity of a group representation

A simple question on groups and quotient spaces.

A representation induced from one subgroup and restricted to another

A morphism intertwining two induced representations

Morphisms of two fully reducible representations of a group

Special functions, Fourier series

Restriction of an Induced Representation

The Hausdorffness of a locally compact topological group

Functions on a group. Functions of the inverse element.

Two definitions of complete algebraic reducibility are equivalent by Zorn's lemma. Does this equivalence stay for topological spaces?

Continuity in topology. An example from Nakahara's book

Splitting of a topological vector space (TVS) into an uncountable number of subspaces

On the definition of Banach space

Complete reducibility, in linear algebra and in topology

On the definition of local compactness

A topological detail in the definition of Lie group

Topological space, manifold, open sets

Is a Radon measure always positive on non-empty open sets? The same question about the Haar measure.

Functions mapping a group to a Hilbert space.

Induced representations built on sections of an associated vector bundle. Questions on notations

A detail in the proof of Schur's lemma: the closures of the $\ker$ and $\operatorname{img}$ of the intertwiner.

Complement to a subspace, in linear algebra, in topology, in functional analysis