Show that the characters of the representations $phi_n$ of $SU(2)$ constitute a complete orthogonal set. The 2019 Stack Overflow Developer Survey Results Are In Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Prove or disprove: the Hilbert-Schmidt norm is independent of the choice of basis on $mathbbR^n$Question 4, chapter III, section 7 in Vinberg “Linear representations of groups. ”Use the theory of characters to derive the following relation for the representations of $SU_2.$prove that any central function of $SU_2$ is uniquely determined by its restriction to the following subgroup.A discrepancy in understanding a solution given to me here for a problem of Vinberg section 8.The number of irreducible representationsHow to show trace of $AB$ is zero for $A in mathfraku_n$ and $B in mathcalH_n$?One dimensional representations of the plane orthogonal group $O(2)$.Relation between finite abelian group and its set of linear charactersProof verification regarding supremum of a setproof of “conjugacy theorem of BSA” following HumphreysShow that the mapping $x^*mapsto x^*(x)+r$ is weak$^*$ continuousWhat would be an example of characters forming a complete, orthogonal basis for class functions?Prove that every irreducible real representation of an abelian group is one or two dimensional.A discrepancy in understanding a solution given to me here for a problem of Vinberg section 8.
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Show that the characters of the representations $phi_n$ of $SU(2)$ constitute a complete orthogonal set.
The 2019 Stack Overflow Developer Survey Results Are In
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Prove or disprove: the Hilbert-Schmidt norm is independent of the choice of basis on $mathbbR^n$Question 4, chapter III, section 7 in Vinberg “Linear representations of groups. ”Use the theory of characters to derive the following relation for the representations of $SU_2.$prove that any central function of $SU_2$ is uniquely determined by its restriction to the following subgroup.A discrepancy in understanding a solution given to me here for a problem of Vinberg section 8.The number of irreducible representationsHow to show trace of $AB$ is zero for $A in mathfraku_n$ and $B in mathcalH_n$?One dimensional representations of the plane orthogonal group $O(2)$.Relation between finite abelian group and its set of linear charactersProof verification regarding supremum of a setproof of “conjugacy theorem of BSA” following HumphreysShow that the mapping $x^*mapsto x^*(x)+r$ is weak$^*$ continuousWhat would be an example of characters forming a complete, orthogonal basis for class functions?Prove that every irreducible real representation of an abelian group is one or two dimensional.A discrepancy in understanding a solution given to me here for a problem of Vinberg section 8.
$begingroup$
The question is given below:
And the other questions mentioned are (I know the solutions of all of them):
Sorry for the bad formulation of the my question at the first time I have edited it
I think I should use this theorem in the proof of the first part:
As I know that $SU_2$ is a compact topological group and I know that $Phi_n$ is a series of irreducible complex representation of $SU_2$ then their matrix elements form a complete orthogonal set in the space $C_2(SU_2)$ by the theorem where $C_2(X)$ denote infinite dimensional hermitian space. My problem is that the question requires the complete orthonormal set in the space of continuous central functions on SU_2 , could anyone help me in showing this please?
Also for the second part of the question I do not know how to show it from the following givens (especially the three problems the author require me to used), could anyone help me please in this part?
proof-verification representation-theory lie-groups lie-algebras characters
asked Apr 6 at 14:30
hopefullyhopefully
231215
$endgroup$
This question has an open bounty worth +50
reputation from Idonotknow ending ending at 2019-04-15 15:11:13Z">tomorrow.
The question is widely applicable to a large audience. A detailed canonical answer is required to address all the concerns.
|
show 10 more comments
$begingroup$
The question is given below:
And the other questions mentioned are (I know the solutions of all of them):
Sorry for the bad formulation of the my question at the first time I have edited it
I think I should use this theorem in the proof of the first part:
As I know that $SU_2$ is a compact topological group and I know that $Phi_n$ is a series of irreducible complex representation of $SU_2$ then their matrix elements form a complete orthogonal set in the space $C_2(SU_2)$ by the theorem where $C_2(X)$ denote infinite dimensional hermitian space. My problem is that the question requires the complete orthonormal set in the space of continuous central functions on SU_2 , could anyone help me in showing this please?
Also for the second part of the question I do not know how to show it from the following givens (especially the three problems the author require me to used), could anyone help me please in this part?
proof-verification representation-theory lie-groups lie-algebras characters
asked Apr 6 at 14:30
hopefullyhopefully
231215
$endgroup$
This question has an open bounty worth +50
reputation from Idonotknow ending ending at 2019-04-15 15:11:13Z">tomorrow.
The question is widely applicable to a large audience. A detailed canonical answer is required to address all the concerns.
$begingroup$
What is 7.4? which book is this from?
$endgroup$
– Sheve
Apr 6 at 15:13
$begingroup$
Ernest B. Vinberg ..... "Linear representations of groups "@Sheve
$endgroup$
– hopefully
Apr 6 at 15:20
1
$begingroup$
@Sheve math.stackexchange.com/questions/3166964/…
$endgroup$
– hopefully
Apr 6 at 15:41
$begingroup$
@Sheve and this is a solution ofanother one problem of the problems mentioned math.stackexchange.com/questions/3168577/…
$endgroup$
– hopefully
Apr 6 at 22:41
1
$begingroup$
* this follows immediately since all trace functions (characters) are central
$endgroup$
– Sheve
19 hours ago
|
show 10 more comments
$begingroup$
The question is given below:
And the other questions mentioned are (I know the solutions of all of them):
Sorry for the bad formulation of the my question at the first time I have edited it
I think I should use this theorem in the proof of the first part:
As I know that $SU_2$ is a compact topological group and I know that $Phi_n$ is a series of irreducible complex representation of $SU_2$ then their matrix elements form a complete orthogonal set in the space $C_2(SU_2)$ by the theorem where $C_2(X)$ denote infinite dimensional hermitian space. My problem is that the question requires the complete orthonormal set in the space of continuous central functions on SU_2 , could anyone help me in showing this please?
Also for the second part of the question I do not know how to show it from the following givens (especially the three problems the author require me to used), could anyone help me please in this part?
proof-verification representation-theory lie-groups lie-algebras characters
asked Apr 6 at 14:30
hopefullyhopefully
231215
$endgroup$
The question is given below:
And the other questions mentioned are (I know the solutions of all of them):
Sorry for the bad formulation of the my question at the first time I have edited it
I think I should use this theorem in the proof of the first part:
As I know that $SU_2$ is a compact topological group and I know that $Phi_n$ is a series of irreducible complex representation of $SU_2$ then their matrix elements form a complete orthogonal set in the space $C_2(SU_2)$ by the theorem where $C_2(X)$ denote infinite dimensional hermitian space. My problem is that the question requires the complete orthonormal set in the space of continuous central functions on SU_2 , could anyone help me in showing this please?
Also for the second part of the question I do not know how to show it from the following givens (especially the three problems the author require me to used), could anyone help me please in this part?
proof-verification representation-theory lie-groups lie-algebras characters
proof-verification representation-theory lie-groups lie-algebras characters
asked Apr 6 at 14:30
hopefullyhopefully
231215
asked Apr 6 at 14:30
hopefullyhopefully
231215
edited yesterday
hopefully
asked Apr 6 at 14:30
hopefullyhopefully
231215
asked Apr 6 at 14:30
hopefullyhopefully
231215
asked Apr 6 at 14:30
hopefullyhopefully
231215
231215
This question has an open bounty worth +50
reputation from Idonotknow ending ending at 2019-04-15 15:11:13Z">tomorrow.
The question is widely applicable to a large audience. A detailed canonical answer is required to address all the concerns.
This question has an open bounty worth +50
reputation from Idonotknow ending ending at 2019-04-15 15:11:13Z">tomorrow.
The question is widely applicable to a large audience. A detailed canonical answer is required to address all the concerns.
$begingroup$
What is 7.4? which book is this from?
$endgroup$
– Sheve
Apr 6 at 15:13
$begingroup$
Ernest B. Vinberg ..... "Linear representations of groups "@Sheve
$endgroup$
– hopefully
Apr 6 at 15:20
1
$begingroup$
@Sheve math.stackexchange.com/questions/3166964/…
$endgroup$
– hopefully
Apr 6 at 15:41
$begingroup$
@Sheve and this is a solution ofanother one problem of the problems mentioned math.stackexchange.com/questions/3168577/…
$endgroup$
– hopefully
Apr 6 at 22:41
1
$begingroup$
* this follows immediately since all trace functions (characters) are central
$endgroup$
– Sheve
19 hours ago
|
show 10 more comments
$begingroup$
What is 7.4? which book is this from?
$endgroup$
– Sheve
Apr 6 at 15:13
$begingroup$
Ernest B. Vinberg ..... "Linear representations of groups "@Sheve
$endgroup$
– hopefully
Apr 6 at 15:20
1
$begingroup$
@Sheve math.stackexchange.com/questions/3166964/…
$endgroup$
– hopefully
Apr 6 at 15:41
$begingroup$
@Sheve and this is a solution ofanother one problem of the problems mentioned math.stackexchange.com/questions/3168577/…
$endgroup$
– hopefully
Apr 6 at 22:41
1
$begingroup$
* this follows immediately since all trace functions (characters) are central
$endgroup$
– Sheve
19 hours ago
$begingroup$
What is 7.4? which book is this from?
$endgroup$
– Sheve
Apr 6 at 15:13
$begingroup$
What is 7.4? which book is this from?
$endgroup$
– Sheve
Apr 6 at 15:13
$begingroup$
Ernest B. Vinberg ..... "Linear representations of groups "@Sheve
$endgroup$
– hopefully
Apr 6 at 15:20
$begingroup$
Ernest B. Vinberg ..... "Linear representations of groups "@Sheve
$endgroup$
– hopefully
Apr 6 at 15:20
1
1
$begingroup$
@Sheve math.stackexchange.com/questions/3166964/…
$endgroup$
– hopefully
Apr 6 at 15:41
$begingroup$
@Sheve math.stackexchange.com/questions/3166964/…
$endgroup$
– hopefully
Apr 6 at 15:41
$begingroup$
@Sheve and this is a solution ofanother one problem of the problems mentioned math.stackexchange.com/questions/3168577/…
$endgroup$
– hopefully
Apr 6 at 22:41
$begingroup$
@Sheve and this is a solution ofanother one problem of the problems mentioned math.stackexchange.com/questions/3168577/…
$endgroup$
– hopefully
Apr 6 at 22:41
1
1
$begingroup$
* this follows immediately since all trace functions (characters) are central
$endgroup$
– Sheve
19 hours ago
$begingroup$
* this follows immediately since all trace functions (characters) are central
$endgroup$
– Sheve
19 hours ago
|
show 10 more comments
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$begingroup$
What is 7.4? which book is this from?
$endgroup$
– Sheve
Apr 6 at 15:13
$begingroup$
Ernest B. Vinberg ..... "Linear representations of groups "@Sheve
$endgroup$
– hopefully
Apr 6 at 15:20
1
$begingroup$
@Sheve math.stackexchange.com/questions/3166964/…
$endgroup$
– hopefully
Apr 6 at 15:41
$begingroup$
@Sheve and this is a solution ofanother one problem of the problems mentioned math.stackexchange.com/questions/3168577/…
$endgroup$
– hopefully
Apr 6 at 22:41
1
$begingroup$
* this follows immediately since all trace functions (characters) are central
$endgroup$
– Sheve
19 hours ago