bio  website  people.virginia.edu/~btw4e 

location  Charlottesville, VA  
age  33  
visits  member for  5 years, 9 months 
seen  2 hours ago  
stats  profile views  18,655 
I'm an Assistant Professor at the University of Virginia. My interests are geometric representation theory, knot homology and categorification.
2h

answered  JacobsonMorozov theorem 
3h

comment 
JacobsonMorozov 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 $M(n2)$. The space $Hom(M(n2),M(n)$ is 1d 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 offhand 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 4manifold with $H^1(M;\Bbb Z_2)=\Bbb Z_2$ and nonzero cup product $H^1\times H^1\to H^2$
Any closed manifold has nonzero 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 