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visits | member for | 5 years, 2 months |
seen | Dec 19 at 17:37 | |
stats | profile views | 2,952 |
Dec 17 |
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automorphism of prime order for group of Lie type in
There's an automorphism of Spin(8), of order 3, that does not preserve any pinning. Its fixed-point subgroup is SL(3). I don't know whether it exists in characteristic 3. There is a nice treatment of all characteristic zero examples at www2.bc.edu/mark-reeder/Torsion.pdf |
Dec 14 |
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Does the $(\mathbb Z/2)$-graded isomorphism $E_n \cong E_{n+2}$ have any nice properties?
I didn't mean anything too metaphysical. Since the two-periodic E_n and E_{n+2} operads have actions of O(n) and O(n+2), something you could add to your list of hypothetical "nice properties" is that the isomorphism between them is equivariant for the inclusion O(n) --> O(n+2). Is that true? |
Dec 14 |
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Does the $(\mathbb Z/2)$-graded isomorphism $E_n \cong E_{n+2}$ have any nice properties?
Is there a single operad called E_n? Or is there an interesting connected space of operads called E_n with no distinguished base point? For the nonlinear version (operads in spaces), I hope that the "classifying space of E_n operads" is BO(n). The classifying space of E_n operads in your funny 2-periodic category must be a lot different. Maybe it is BO? |
Nov 24 |
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Is there a cotangent bundle of a stable $\infty$-category?
Thanks Sam. What if I insist that the construction of $T^* C$ should not depend on any monoidal structure $\otimes$? For example it doesn't seem like such a structure is available in part 2. |
Nov 21 |
awarded | Nice Question |
Nov 20 |
asked | Is there a cotangent bundle of a stable $\infty$-category? |
Nov 8 |
accepted | When does a cubic surface pass through five lines? |
Nov 7 |
awarded | Popular Question |
Nov 6 |
asked | When does a cubic surface pass through five lines? |
Nov 6 |
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RO(G) grading of Mackey functors
In characteristic zero the category of Mackey functors is semisimple. The simple Mackey functors over any field have been classified by Thevenaz and Webb -- they are one-to-one with conjugacy classes of pairs (subgroup $H$, irrep $L$ of $N_G(H)/H$). I think a sphere $\,\, S^V$ acts on the simple Mackey functor corresponding to $(H,L)$ by a shift, but a shift that depends on $H$: the dimension of the fixed-point space $V^H$. |
Nov 1 |
awarded | Nice Question |
Oct 23 |
awarded | Yearling |
Jul 2 |
awarded | Curious |
Oct 23 |
awarded | Yearling |
Apr 11 |
awarded | Nice Question |
Mar 12 |
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What are some triangulations of Grassmannians?
I have nothing against Schubert cells, but the attaching maps are very complicated. I would be just as interested in hearing about a regular cell complex structure as a triangulation, but it's easy to get from one to the other so I asked about triangulations. If you know a triangulation that refines the Schubert stratification, so much the better! |
Mar 12 |
asked | What are some triangulations of Grassmannians? |
Nov 16 |
awarded | Popular Question |
Oct 23 |
awarded | Yearling |
Oct 13 |
comment |
The highest root of an ADE quiver
I was a little off: a nontrivial irrep matches to O(-1) on a reduced P^1. The trivial irrep matches to the structure sheaf of the scheme-theoretic exceptional fiber, shifted by 1. More stuff like this available here arxiv.org/abs/math/9812016 |