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 Inquisitive
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Oct
4
accepted Why is $\mathfrak{h}$ assumed to be an abelian Lie algebra in this lemma?
Oct
4
accepted Why is $\operatorname{Hom}_{\textrm{AG}}(k^\times,k^\times)\cong\mathbb{Z}$?
Oct
4
comment Why is $\operatorname{Hom}_{\textrm{AG}}(k^\times,k^\times)\cong\mathbb{Z}$?
Oh right, this is a special case that $GL_n(k)$ is an affine subvariety of $k^{n^2+1}$. Thanks.
Oct
4
revised Why is $\operatorname{Hom}_{\textrm{AG}}(k^\times,k^\times)\cong\mathbb{Z}$?
deleted 1 character in body
Oct
4
asked Why is $\operatorname{Hom}_{\textrm{AG}}(k^\times,k^\times)\cong\mathbb{Z}$?
Sep
30
revised Kac's Infinite Dimensional Lie Algebras, Lemma 1.6
edited body
Sep
30
comment Kac's Infinite Dimensional Lie Algebras, Lemma 1.6
Thank you David.
Sep
30
accepted Kac's Infinite Dimensional Lie Algebras, Lemma 1.6
Sep
30
asked Kac's Infinite Dimensional Lie Algebras, Lemma 1.6
Sep
27
asked Why is $\mathfrak{h}$ assumed to be an abelian Lie algebra in this lemma?
Sep
26
awarded  Inquisitive
Sep
25
accepted If $\mathcal{C}$ is a monoidal, $R$-linear category, what does the notation $\mathcal{C}\otimes_R\bar{R}$ mean, if $\bar{R}$ a quotient of $R$?
Sep
25
asked If $\mathcal{C}$ is a monoidal, $R$-linear category, what does the notation $\mathcal{C}\otimes_R\bar{R}$ mean, if $\bar{R}$ a quotient of $R$?
Sep
18
asked Finite dimensional $kH_n$-module as direct sum of spaces on which $X_i-v_i$ acts locally nilpotently?
Sep
10
accepted What is the group action of $\prod_i S_{n_i}$ making $\{h\in S_n:h(v)=v'\}$ a principal homogeneous set?
Sep
9
comment What is the group action of $\prod_i S_{n_i}$ making $\{h\in S_n:h(v)=v'\}$ a principal homogeneous set?
Thanks David, Explicilty, how does $\gamma_i$ define the embedding $W\hookrightarrow (S_n)_\nu$? If $(\sigma_i)_i\in W$ is a tuple of permutations $\sigma_i\in S_{n_i}$, does it map to the permutation in $S_n$ defined by acting as $\sigma_i$ on the subset of $n_i$ indices of the coordinates which equal $i$? Since these indices partition $\{1,\dots,n\}$, this makes sense.
Sep
8
asked What is the group action of $\prod_i S_{n_i}$ making $\{h\in S_n:h(v)=v'\}$ a principal homogeneous set?
Aug
31
comment Quiver algebra as a wreath product?
Anyway, I think you're second comment is what I'm after. Is the semidirect product of $A^{\otimes n}$ and $kS^n$ the set $A^{\otimes n}\otimes kS_n$ with usual addition but multiplication on $A\wr S_n$ given by $(a_1\otimes\cdots\otimes a_n\otimes \sigma)(b_1\otimes\cdots\otimes b_n\otimes\tau)=(a_1b_{\sigma(1)}\otimes\cdots\otimes a_nb_{\sigma(n)}\otimes \sigma\tau)$?
Aug
31
comment Quiver algebra as a wreath product?
@Aaron You're right, sorry, I mean to ask about the quiver Hecke algebra. I'm reading the paper Quiver Hecke Algebras and 2-Lie Algebras by Rouquier, and this is Section 3.2 on page 12. The notation $k[x]^\Omega$, is not defined, so I'm guessing it's tuples with coordinates in $k[x]$, indexed by elements of $\Omega$. I thought $S_n$ would act on $(p(x)_\alpha,p(x)_\beta,\dots,p(x)_\eta)\in k[x]^{\Omega^n}$ by $S_n$ acting on the the $n$-tuples in $\Omega$ $\alpha,\beta...\in\Omega^n$ by permuting the usual indices $1,\dots,n$ there.
Aug
31
revised Quiver algebra as a wreath product?
edited title