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GL OH - Shared screen with speaker view
bezrukav
35:06
what’s n in E_n?
Sam Raskin
35:15
2
bezrukav
35:27
thanks!
Tony Feng
39:03
In “factorization algebras = E_n algebras” does the curve also need to be A^1
Lin Chen
39:16
R^n
Sam Raskin
39:41
The statement in topology is that translation-invariant factorization cosheaves on R^n are the same as E_n-algebras.
Alexander Braverman
46:42
Does anybody know if Lurie's theorem is still true if you replace Rep_q(T) by some other braided monoidal category?
Lin Chen
50:16
Lurie’s theorem is the combination of two things: (1) E_2 vs factorization on R^2 (2) Drinfeld center vs E_2. The second part can be generalized to any ambient presentable E_2-category.
Alexander Braverman
51:15
So the answer is yes, right?
Sam Raskin
51:16
Sasha, in a sense, morally yes, but the point of using that category is that you have a good notion of positivity. Essentially, you want to use positivity to get simple Koszul duality statements (this is where Hopf algebras appear: you Koszul dualize the coalgebra structure to get an E_2-algebra). So it wouldn’t work as beautifully.
gurbir
52:27
(t-exact at negative level)
Alexander Braverman
53:34
I have a particular example in mind - in that case Rep_q(T) is replaced by Rep_q(GL(n)\times GL(m)) and some particular Hopf algebra there
Sam Raskin
01:11:57
That distinction can be absorbed into the definitions and is a little more subtle.
Dennis Gaitsgory
01:15:17
casselman-shalika: Frenkel-G-Vilonen
Roman Travkin
01:24:46
The convolution in the coherent RHS should, I guess, correspond to some kind of fusion…
Dennis Gaitsgory
01:25:48
let’s discuss this!
Dennis Gaitsgory
01:27:22
in fact, if you think of LocSys, this convolution has no meaning
Sam Raskin
01:27:51
Convolution doesn’t preserve the support condition….
Roman Travkin
01:30:30
Sam, yeah, maybe restrict to support at 1…
Roman Travkin
01:33:32
Dennis, why—doesn’t the factorization str give us the fusion over C?
Roman Travkin
01:34:43
On LocSys(D^\circ)
Justin
01:38:04
Isn't it true that under the iso G^/G = LS^, convolution in QCoh goes over to fusion?
Roman Travkin
01:42:43
that’s what I’d think…
Dennis Gaitsgory
01:43:18
I don’t think so, but maybe am wrong
Justin
01:50:17
If we use Betti local systems, then we have LS = Map(S^1,pt/G) = G/G and I thought the E_2 structure on the LHS corresponds to convolution on the RHS