"Sagittarius A* (pronounced "Sagittarius A-Star", abbreviated Sgr A*) is a bright and very compact astronomical radio source at the Galactic Center of the Milky Way. It is located near the border of the constellations Sagittarius and Scorpius, about 5.6° south of the ecliptic, visually close to the Butterfly Cluster (M6) and Shaula. Sagittarius A* is the location of a supermassive black hole, similar to massive objects at the centers of most, if not all, spiral and elliptical galaxies."
https://en.wikipedia.org/wiki/Sagittarius_A*
We can never ever travel to the center of the galaxy and verify there is a "black hole" there. Does this mean we should stop asking questions about the Sagittarius A star? Should it be a "crime" to ask questions about the Sagittarius A star? Should it be a "crime" to disagree on the nature of the Sagittarius A star?
Earlier I wrote some posts at MO under the username "user122276" but I chose to delete my profile - I disagree with the way the forum was administered:
"When someone else is editing my posts and include links that I do not like, this is to show me disrespect as I have explained earlier. And one of the cardinal rules on this forum is that you should respect other users and their choices. When I request that you respect my choices and do not edit my posts and you violate this, you violate the rules of the forum in my opinion. – user122276"
https://mathoverflow.net/questions/391931/which-representations-of-mathfraksl2-are-homomorphic-images-of-the-tensor/392578#comment1025085_392578
https://mathoverflow.net/questions/385099/when-do-flat-holomorphic-connections-exist
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Downloading from the arXiv site and uncompressing @VomitIT-ChunkyMessStyle - it did install. Thanks. |
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asked | Downloading from the arXiv site and uncompressing |
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awarded | Autobiographer |
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awarded | Autobiographer |
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Tensor product of irreducible representation of $\mathfrak{sl_3}$ ..hence if $V_1,..,V_k$ are the irreducible components of $W$ and $ \sigma \in S_k$ is a permutation, you may write $W \cong V_1 \oplus \cdots \oplus V_k \cong V_{\sigma(1)} \oplus \cdots \oplus V_{\sigma(k)}$. I believe it is "common practice" to refer to these two decompositions as "the canonical decomposition" into irreducibles. |
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Tensor product of irreducible representation of $\mathfrak{sl_3}$ @Callum - "canonical" mean you may "permute" the irreducible components. If $W \cong V_1 \oplus V_2$ is the decomposition of $W$ into irreducibles, we may also write $W \cong V_2 \oplus V_1$. I assume this is what you are speaking about. |
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Does $Spec(k[G/[P,P]])$ have worse than quotient singularities? The affinization map $G/[P,P] \rightarrow S:=Spec(k[G/[P,P])$ is an isomorphism iff $G/[P,P]$ is an affine scheme, and in this case $S$ is regular, hence for the scheme $S$ to be singular one must have $G/[P,P]$ non-affine. What is the reason for studying this ring for $G/[P,P]$? |
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Is there a computationally cleaner way of working with inverse image functor $f^{-1}\mathcal{O}_Y$ in the category of schemes? To "take the topological pullback" to an open subscheme equals "restriction". |
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Feb
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Is there a computationally cleaner way of working with inverse image functor $f^{-1}\mathcal{O}_Y$ in the category of schemes? If $i:=Spec(A):=V \rightarrow X$ is the inclusion of an open affine in $X$ it follows there is an isomorphism of sheaves $i^{-1}(\mathcal{O}_X) \cong \mathcal{O}_V$. Hence $H^0(V, i^{-1}(\mathcal{O}_X)) \cong A$. |
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Does $Spec(k[G/[P,P]])$ have worse than quotient singularities? Note: The scheme $G/[P,P]$ is a regular quasi projective scheme of finite type over the base field. |
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Does $Spec(k[G/[P,P]])$ have worse than quotient singularities? There is an inclusion $[P,P] \subseteq P$ and a surjective morphism $\pi: G/[P,P] \rightarrow G/P$. What type of a "fibration" is $\pi$ in the case of the grassmannian or projective space? For projective space there is the $\mathbb{G}_m$-principal fiber bundle $\rho: \mathbb{A}^{n+1}_k-\{(0)\} \rightarrow \mathbb{P}^n_k$. Is $\rho$ related to $\pi$? |
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Jan
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What scaling really means mathematically? added 639 characters in body |
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Jan
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Is there a computationally cleaner way of working with inverse image functor $f^{-1}\mathcal{O}_Y$ in the category of schemes? "I doubt something as clean would hold in generality, but is there any argument I can make in specific cases that allows me to avoid working with the definition directly? In particular, I'd be very interested in the case of the definition of the pull back of a sheaf $G$ of $\mathcal{O}_Y$ modules: $$f^*G=f^{-1}G\otimes_{f^{-1}\mathcal{O}_Y}\mathcal O_X$$ which feels incredibly unwieldy to work with from the raw definitions." - you should be more specific - what exactly are you looking for? |
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Projective spaces: why adding points to make linear intersections work make everything else work too? added 437 characters in body |
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Projective spaces: why adding points to make linear intersections work make everything else work too? added 588 characters in body |
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awarded | Custodian |
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Projective spaces: why adding points to make linear intersections work make everything else work too? added 327 characters in body |
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Why is Serre duality compatible with $G$-actions of linear algebraic groups? ..and given an injective resolution $W \rightarrow I_i$ as $P$-modules, you may ask if the induced sequence $E(W) \rightarrow E(I_i)$ is an injective resolutions of linearized vector bundles on $G/P$. |
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Does $Spec(k[G/[P,P]])$ have worse than quotient singularities? how does $k[G/[P,P])$ look like when $G/P:=SL(V)/P \cong \mathbb{G}(m,n)$ is the grassmannian? |
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Example 2.13 in Wells "Differential Analysis on Complex Manifolds" Conclusion added 301 characters in body |