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Question 1

3votes

0answers

47views

Injectivity of derivations from the middle transvectant in the free Lie algebra on $\operatorname{Sym}^m$ for $\mathrm{SL}_2$

Let $G=\mathrm{SL}_2(\mathbb C)$, $V$ its standard representation, and $V_m=\operatorname{Sym}^m(V)$ with $m\equiv 2 \pmod 4$. It is classical that$$\Lambda^2 V_m \;\cong\; \bigoplus_{\substack{1\le ...

kindasorta

3,366

askedyesterday

Question 2

2votes

0answers

142views

Rewriting a quaternary cubic as sums of $5$ cubes of linear forms

This question was first asked here but got no answer.This paper by R. Garver talks about removing 4 terms from the 9th degree equation. Although everything is easy to understand, there was an ...

Thinh Dinh

196

askedAug 13 at 3:51

Question 3

2votes

1answer

259views

Invariance of averages of cubic forms

This is a follow-up discussion to a previous question, posted as a separate question following the suggestion of Stanley Yao Xiao.The question is about a particular passage in Bhargava-Shankar-...

user564434

187

askedMay 24 at 22:12

Question 4

6votes

1answer

395views

Integrals of cubic forms around the unit circle

Given a nondegenerate real cubic form $f(x,y)$ in two variables, consider the integral$$I(f) = \frac{|\mathrm{Disc}(f)|^{1/6}}{2\pi} \int_0^{2\pi} f(\cos(\theta),\sin(\theta))^{-2/3} \, d\theta$$The ...

user564434

187

askedMay 24 at 10:33

Question 5

1vote

0answers

74views

Exploit realization of Lie super algebra

It is known in the context of Clifford analysis $\mathbb{R}_m$ that the operator $\underline{x}$ and $\overline\partial$ generate the Lie superalgebra $\mathfrak{osc}(1\vert2)$, where $\underline{x}=...

Jules Binet

131

askedApr 9 at 13:17

Question 6

4votes

1answer

169views

Invariants of (complex) vectors under simultaneous $\mathrm{SO}_n$ action?

$\DeclareMathOperator\SO{SO}$Consider the natural action of $G=\SO_n$ on $\mathbb{C}^n$. What are the polynomial invariants of vectors under simultaneous rotations by $\SO_n$, i.e. which $P(v_1,v_2,\...

Another User

235

askedApr 4 at 13:11

Question 7

2votes

0answers

143views

Sufficient conditions to prove invariance of a state of a $C^$ algebra under a group $G$ of $$-automorphisms

This is a follow-up question of a previous question that I asked on Math Stack Exchange: Doubt on invariant states and asymptotic abelianess, where it is observed that having a state $\omega$ over a $...

MBlrd

181

askedMar 26 at 20:34

Question 8

4votes

1answer

328views

Invariants of a maximal unipotent group in GL(n) acting by conjugation on n by n matrices

Let $G = \operatorname{GL}(n, \mathbb{C})$ and let $U \subset G$ be the usual maximal unipotent subgroup (upper triangular matrices with ones on the diagonal). Let $U$ act by conjugation on the space $...

user558182

41

askedMar 24 at 22:02

Question 9

0votes

0answers

79views

Fully determined set of equations in coefficients of an unknown polynomial with given discriminant

A polynomial $f \in \mathbb{Z}[x]$ of degree $d$, in general has $d+1$ coefficients. Suppose I know $f$ has discriminant $N \in \mathbb{Z}$. That is one (nonlinear) equation in $d+1$ unknowns using ...

Oisin Robinson

273

askedMar 5 at 21:48

Question 10

2votes

0answers

157views

Doubt on invariant states on C*-algebras

I am reading "Operator algebras and quantum statistical mechanics" by Bratteli and Robinson, and I have one doubt regarding the definition of invariant states under a group $G$ of $*$ - ...

MBlrd

181

askedFeb 15 at 12:02

Question 11

8votes

1answer

366views

Commuting variety and invariant polynomials

Let $\mathfrak{h}$ be a Cartan subalgebra of $\mathfrak{sl}_n\mathbb{C}$, and let $S_n$ denote the Weyl group of $(\mathfrak{sl}_n\mathbb{C}, \mathfrak h)$. I am interested in understanding the ...

Satoshi Nawata

2,373

askedFeb 13 at 10:43

Question 12

10votes

0answers

322views

Is Noether's Problem undecidable?

I begin by recalling Noether's problem over $\mathbb{Q}$:Let $G$ be a finite group that act faithfully by field automorphisms on $\mathbb{Q}(x_1,\ldots,x_n)$, with the action on $\mathbb{Q}$ trivial. ...

jg1896

3,756

askedFeb 13 at 8:40

Question 13

1vote

0answers

165views

A noncommutative analogue of GIT quotient by a finite group

Let $\Lambda$ be a commutative Noetherian ring, and an affine algebra over a certain base field $k$. Let $G$ be a finite group of automorphisms of $\Lambda$, and let $X$ be the affine scheme $\...

jg1896

3,756

askedFeb 4 at 3:15

Question 14

2votes

0answers

83views

Existence of quasi-invariant smooth function with eigencharacter for reductive Lie group

What is known about existence of quasi-invariant smooth function with some eigencharacter on Lie algebra of a reductive Lie group? Consider reductive Lie group $G$ and its Lie algebra $\mathfrak{g}$. ...

Kevin

131

askedFeb 1 at 12:40

Question 15

5votes

0answers

75views

Generators and relations for invariants of the Weyl algebra

Let $k$ be an algebraically closed field of zero characteristic, and $A_n=k\langle x_1, \ldots, x_n, \partial_1, \ldots, \partial_n \rangle$ the rank n Weyl algebra, which can also be described as a ...

jg1896

3,756

askedJan 25 at 11:25

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Stack Exchange Network

Questions tagged [invariant-theory]

Injectivity of derivations from the middle transvectant in the free Lie algebra on $\operatorname{Sym}^m$ for $\mathrm{SL}_2$

Rewriting a quaternary cubic as sums of $5$ cubes of linear forms

Invariance of averages of cubic forms

Integrals of cubic forms around the unit circle

Exploit realization of Lie super algebra

Invariants of (complex) vectors under simultaneous $\mathrm{SO}_n$ action?

Sufficient conditions to prove invariance of a state of a $C^$ algebra under a group $G$ of $$-automorphisms

Invariants of a maximal unipotent group in GL(n) acting by conjugation on n by n matrices

Fully determined set of equations in coefficients of an unknown polynomial with given discriminant

Doubt on invariant states on C*-algebras

Commuting variety and invariant polynomials

Is Noether's Problem undecidable?

A noncommutative analogue of GIT quotient by a finite group

Existence of quasi-invariant smooth function with eigencharacter for reductive Lie group

Generators and relations for invariants of the Weyl algebra

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