4
votes
0answers
125 views

What are global sections of the determinant bundle on the Beilinson-Drinfeld Grassmannian?

Let $X$ be a smooth proper algebraic curve over $\mathbb{C}$, and let $G$ be a reductive group over $\mathbb{C}$. Let $Gr_{X,n}$ be the Beilinson-Drinfeld Grassmannian (for n points in $X$), which ...
2
votes
1answer
86 views

Is is possible to lift an equivariant map of Loop lie algebras to an equivariant map of Loop groups?

For brevity, let $LG=\mathbb{T}\ltimes \tilde{L}G$, the affine loop group and let $G$ be a simple simply conneceted Lie group. I have a map $\phi:L\mathfrak{g} \to L\mathfrak{g}$ that is equivariant. ...
1
vote
0answers
107 views

Are Generalized Verma modules natural w.r.t isometries?

Let $H$ be a subgroup of $G$ with Lie algebras $\mathfrak{h}$ and $\mathfrak{g}$ respectively. If I have 2 representations $V, W$ of $\mathfrak{h}$ equipped with a $\mathfrak{h}$ invariant inner ...
2
votes
1answer
262 views

Kac Moody algebra defintion

Why is the dimension of the cartan subalgebra $2n-\text{rank}(A)$ in the defintion from Kumar's book. From a few examples I can see why the defintion is the way it is, but, I would like a better ...
7
votes
1answer
221 views

Restriction of highest-weight representations to Heisenberg subalgebras

Let $\mathfrak{g}$ be a finite-dimensional complex simple Lie algebra and $\tilde{\mathfrak{g}}=\mathfrak{g}((t))\oplus \mathbf{C}K\oplus \mathbf{C}d$ its Kac-Moody extension ($K$ is the level and $d$ ...
5
votes
1answer
298 views

Is the centralizer of a torus in a Kac-Moody algebra always a Borcherds algebra?

If one has a finite dimension simple Lie algebra, one can easily calculate that taking the centralizer of a torus (or toral subalgebra), that is, summing the weight spaces that lie in some proper ...
6
votes
4answers
401 views

level 2,3 characters of affine su(2)

Does anyone know where I can find an explicit formula to compute the level 2 or level 3 characters of affine $su(2)$? I have found several sources that give a formula to compute the level 1 ...
1
vote
0answers
208 views

Does Iwahori subalgebra correspond to any Cartan decomposition for affine Kac-Moody algebra?

Let $\hat{\mathfrak{g}}$ be an affine Kac-Moody algebra which is the central extension of $\mathfrak{g}[t,t^{-1}]$(polynomial version). Consider Iwahori subalgebra $I$. My question is whether $I$ ...