23,821 reputation
469160
bio website people.virginia.edu/~btw4e
location Charlottesville, VA
age 33
visits member for 5 years, 9 months
seen yesterday

I'm an Assistant Professor at the University of Virginia. My interests are geometric representation theory, knot homology and categorification.


2d
comment Characteristic Cycles and Nearby Cycles
I don't think I can answer Q2 precisely, but my understanding is that this is usual connection between filtrations and deformations using Rees modules. That is, I think that Ginzburg's $L_0$ is the Rees module of the V-filtration (suitably interpreted).
2d
revised Characteristic Cycles and Nearby Cycles
edited body
Jul
23
answered Do Iwahori-Hecke algebras come from cohomology classes?
Jul
22
comment Can view the connected component of the Picard scheme $\text{Pic}^0(X)$ as a “kernel” of the first Chern class?
This is explained on Wikipedia: en.wikipedia.org/wiki/Néron–Severi_group
Jul
14
answered What are the “tensor-closed” object of the BGG category $\mathcal{O}$ of a semisimple Lie algebra $\mathfrak{g}$?
Jul
13
awarded  Enlightened
Jul
13
awarded  Nice Answer
Jul
7
awarded  Popular Question
Jul
3
answered Jacobson-Morozov theorem
Jul
3
comment Jacobson-Morozov theorem
@YCor Can you describe how you get $PSL_2$ in $PGL_4$? That nilpotent has a Jordan block of length 2 in the adjoint representation, which shouldn't be possible if it were the $E$ in a $PSL_2$ representation.
Jul
1
comment Is every weight of an integrable highest weight module in the Tits cone?
That is false in all types: you have to be in the same coset of the root lattice as the highest weight. With that proviso, I think it's true. Again, induct on the number of times you've had to subtract positive roots. If the weight $\mu$ isn't dominant, then its conjugate which is dominant will reduce this number, and have the same weight multiplicity. Once it's dominant, I think one should be able to find a simple root such that $\mu+\alpha_i$ is in the polytope (I don't have a slick explanation, but the picture looks right in my head). $E_i$ is injective here, so by induction, QED.
Jun
30
revised Is every weight of an integrable highest weight module in the Tits cone?
edited body
Jun
30
answered Picard group of a quotient of a group by its maximal parabolic subgroup
Jun
30
answered Is every weight of an integrable highest weight module in the Tits cone?
Jun
24
comment Understanding the Weyl Character Formula
@VítTuček No, there are really no maps. Think about $\mathfrak{sl}_2$. You have the Verma $M(n)$ and the Verma $M(-n-2)$. The space $Hom(M(-n-2),M(n)$ is 1-d if $n$ is an integer with $n\geq -1$, and 0 dimensional otherwise.
Jun
23
answered Understanding the Weyl Character Formula
Jun
23
revised Understanding the Weyl Character Formula
deleted 3 characters in body
Jun
16
answered Ext groups in the equivariant derived category
Jun
15
comment Closed orientable 4-manifold with $H^1(M;\Bbb Z_2)=\Bbb Z_2$ and non-zero cup product $H^1\times H^1\to H^2$
Any closed manifold has non-zero cup product by Poincare duality. So $S^1\times S^2$ satisfies your criteria.
Jun
11
answered Do the support sets of subspaces give the representable matroids?