The kac-moody-algebras tag has no wiki summary.

**9**

votes

**0**answers

143 views

### Cohomological Proof of Serre Relations for a Symmetrizable Kac-Moody Algebra

In 'Infinite Dimensional Lie Algebras, 3rd edition', Kac mentions at the top of p. 170 that 'a simple cohomological proof of Theorem 9.11 was found by O. Mathieu (unpublished)'.
Does anyone know how ...

**4**

votes

**0**answers

124 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 ...

**1**

vote

**0**answers

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 ...

**1**

vote

**0**answers

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 $I$ ...