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seen Dec 19 at 17:37

Dec
17
comment 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
comment 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
comment 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
comment 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
comment 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
comment 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