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1d
reviewed Leave Open Is it possible to write down the explicit expressions of some extensions of conformal vector fields on spheres?
1d
reviewed Leave Open weakly p- summable sequence
1d
reviewed Leave Open Can we do better than zero padding of FFT?
1d
comment Why should intersection cohomology and quantum cohomology be related for a symplectic resolution?
@SamHopkins Seems to me that's all the more reason to ask this question :) OTOH, there are random people like me who will be interested in the answer, and there might be random people who know the answer, so I'm glad that OP asked the question here rather than over email.
Feb
6
comment Can the ribbon category of f.d. reps of $\mathcal{U}_q(\mathfrak{sl}(2))$ be modified so the twist is trivial on the vector representation?
@NoahSnyder Ah, yes, that's much clearer.
Feb
6
comment Can the ribbon category of f.d. reps of $\mathcal{U}_q(\mathfrak{sl}(2))$ be modified so the twist is trivial on the vector representation?
@AndyManion Just the vector. Already for the symmetric and exterior squares, the ribbon is something like multiplication by $q$.
Feb
6
comment Is there a finite test for isomorphisms of rigid monoidal abelian categories, part II
Your point being that there is at most one symmetry on $\mathcal C$ such that the functor is symmetric monoidal, but in fact there need not be any such symmetry?
Feb
5
comment Is the bar construction of a CDGA model a Hopf algebra model for the loop space?
Why doesn't your linked question provide the answers you're looking for?
Feb
5
awarded  Nice Question
Feb
4
comment Can the ribbon category of f.d. reps of $\mathcal{U}_q(\mathfrak{sl}(2))$ be modified so the twist is trivial on the vector representation?
Come to think of it, I said "quotient out by the ideal of negligible morphisms", which I do think always works, but I'm going off of memory, and one regularly simplifies claims in memory that are more complicated in real life. If so, then one version of the "local relations" question is whether that ideal is finitely generated.
Feb
4
comment Can the ribbon category of f.d. reps of $\mathcal{U}_q(\mathfrak{sl}(2))$ be modified so the twist is trivial on the vector representation?
... Schur–Weyl duality recently, including by regulars here on MO, which perhaps has answered the question, but I admit I have not kept up to date on the results.
Feb
4
comment Can the ribbon category of f.d. reps of $\mathcal{U}_q(\mathfrak{sl}(2))$ be modified so the twist is trivial on the vector representation?
I should warn: I'm not sure how much of my representation theory claims are on firm footing. Indeed, my impression is that there are (or at least recently were) open questions about whether you actually produce $\mathcal U_q(\mathfrak{gl}(n))$ from following a procedure like I said, or just some category that maps to it. The question is: "is $\mathrm{Rep}(\mathcal U_q\mathfrak g)$ described by local relations"? The Kuperberg spiders give the answer "yes" for the $\mathfrak g$ of rank-2, and for a long time it was open in higher rank. I know that there's been major recent work on quantum...
Feb
4
answered Can the ribbon category of f.d. reps of $\mathcal{U}_q(\mathfrak{sl}(2))$ be modified so the twist is trivial on the vector representation?
Jan
29
comment Is there any work on “super Fukaya categories”?
@ChrisGerig You will have trouble writing down a function with isolated critical points, I think, because the odd directions on a supermanifold are really really small --- too small to have very many functions. For some applications the odd directions feel noncompact, in which case you'd have different Morse complexes depending on the boundary conditions of your Morse function, but for many applications the odd directions feel compact (see "really really small" above). Probably you can construct a Morse--Bott theory. Note that all supermanifolds deformation retract onto their even cores.
Jan
29
comment Is there any work on “super Fukaya categories”?
@AHusain Given my intended interests, I should revisit that case. And come to think of it, I did claim in math.northwestern.edu/~theojf/FloerTheoryNotes.pdf that A-model / Fukaya category arises from a particular gauge-fixing of PSM. But note that that particular discussion requires the branes to be Lagrangian.
Jan
29
asked Is there any work on “super Fukaya categories”?
Jan
28
comment Technical issue in the approach to Lie groups taken in Brian C. Hall's book
Well, looks like you can add (or already have!) my notes to the list of places that skip that very important step.
Jan
28
comment Technical issue in the approach to Lie groups taken in Brian C. Hall's book
But the answer you're probably looking for is that in the semisimple case you should compare Ad(g) to Aut(g). Clearly Ad(G) is a subgroup of Aut(g), which is Zariski-closed in GL(g), and so it suffices to check that they have the same Lie algebra. You prove this in your answer, and I think Mark gave an equivalent argument somewhere in chapter 4, but I can't find it.
Jan
28
comment Technical issue in the approach to Lie groups taken in Brian C. Hall's book
@NoahSnyder That's a good question. The actual answer is that all of chapter 7 is too sketchy, because it's based on Richard's lectures from 2006 (that required a bit of time-travel for me, since I arrived in 2007), and he left out a lot of details. Mark's lectures from 2008 are chapters 1-6, and Mark's lectures were complete, but my notes leave out most proofs in the first two or three chapters.
Jan
27
comment Technical issue in the approach to Lie groups taken in Brian C. Hall's book
If you know that you have a negative-definite Killing form, then the adjoint action maps your group to SO(Lie algebra). I guess it might not have closed image. It also may not be faithful, of course. If you centrally-extend the Lie algebra of a compact group, can you cover this extension by an extension of the group by a torus?