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Apr
21 |
comment |
Computing in quantum groups
Ha. I almost gave this answer with a link to your website. |
Mar
10 |
awarded | Organizer |
Mar
10 |
revised |
Irreducible representations in BGG category $\mathcal{O}$ over (finitely) direct sum of general linear Lie superalgebra
removed ct.category-theory tag, added rt.representation-theory tag. |
Mar
10 |
suggested | approved edit on Irreducible representations in BGG category $\mathcal{O}$ over (finitely) direct sum of general linear Lie superalgebra |
Mar
3 |
awarded | Yearling |
Feb
18 |
comment |
Generalization of the sign representation to Hopf algebras
@DenisNardin In the group case the determinant is $\pm 1$. This is not going to carry over in general. It would be helpful if to see a list of properties that one might want to see in such a sign representation (besides giving the sign rep. in the group case). |
Dec
8 |
answered | Request for classical articles in representation theory |
Dec
5 |
comment |
Mystery behind ADE Dynkin diagram
@JoshuaGrochow I suggest you read the answer to the question linked in Ben's comment. I believe the current question is treated very well there. |
Sep
3 |
revised |
Free $k[x_1, \dots, x_n]^{S_n}$-module?
fixed typo |
Sep
3 |
comment |
What's the relation between half-twists, star structures and bar involutions on Hopf algebras?
Let us continue this discussion in chat. |
Sep
3 |
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What's the relation between half-twists, star structures and bar involutions on Hopf algebras?
The bar involution is an algebra automorphism defined by $\overline{E}=E$, $\overline{F}=F$ and $\overline{q}=q^{-1}$. The relation $[E,F]=(K^2-K^{-2})/(q-q^{-1})$ implies that $\overline{K}=K^{-1}$ since $\overline{[E,F]}=[E,F]$. I guess if ``the star is antilinear'' means take complex conjugates of coefficients, then, for $q$ a root of unity, this would be compatible. |
Sep
3 |
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What's the relation between half-twists, star structures and bar involutions on Hopf algebras?
Maybe I am misunderstanding what you mean by $U_qSL(2)_{\mathbb{C}}$. Is this the quantum group over $\mathbb{C}(q)$, or $U_qSL(2)\otimes_{\mathbb{Q}(q)}\mathbb{C}$ where $\mathbb{C}$ is regarded as a $\mathbb{Q}(q)$ module with $q$ acting as a scalar? |
Sep
3 |
comment |
What's the relation between half-twists, star structures and bar involutions on Hopf algebras?
Are you sure both send $K\mapsto K$? My first thought was that they differ by the bar involution, but then one should be $K\mapsto K^{-1}$. |
Sep
2 |
answered | Free $k[x_1, \dots, x_n]^{S_n}$-module? |
Sep
1 |
revised |
Constructing a simple $A$-module
another typo |
Sep
1 |
revised |
Constructing a simple $A$-module
fixed typo |
Sep
1 |
answered | Constructing a simple $A$-module |
Aug
27 |
comment |
Generalized identities of (soluble) groups
I don't understand your definition. If $a_1,\ldots,a_n\in G$, what does $x^{a_1}\cdots x^{a_n}$, $x\in G$ mean? |
Jul
14 |
comment |
What are the “tensor-closed” object of the BGG category $\mathcal{O}$ of a semisimple Lie algebra $\mathfrak{g}$?
No, I was mistaken. I think one can probably show that the tensor product of a Verma module with an infinite dimensional module is not finitely generated. |
Jul
14 |
comment |
Decomposition of quadratic polynomials inti irreducible representations of affine group over a finit field
@Thomas $V$ is not closed under addition. It is just a set. |