23,565 reputation
468158
bio website people.virginia.edu/~btw4e
location Charlottesville, VA
age 33
visits member for 5 years, 9 months
seen 2 hours ago

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


2h
answered Jacobson-Morozov theorem
3h
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.
1d
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.
2d
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
comment Fundamental theorems of invariant theory, twisted by a representation
My off-hand guess is that this is really hard. Isn't this hard when $n=m=0$? That's understanding the invariants in $\mathrm{Sym}^k(U^*)$ for all $k$, and plethysm is scary.
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?
Jun
10
reviewed Leave Open Codimension one embeddings
Jun
10
reviewed Leave Open Binary Quadratic Forms with coefficients in $F_q[T]$
Jun
2
comment The sum of squared logarithms conjecture
@PraveenKumar It's LateX: en.wikipedia.org/wiki/LaTeX
Jun
2
awarded  Informed
Jun
2
reviewed Leave Open relations in (\mathbb P^1)^n
May
28
reviewed Leave Open The kernel of the natural map $\pi_k(BU(r)) \to \pi_k (BU)$
May
28
reviewed Close Definition of Category of Hypergraphs