For a homogeneous space $M = G/B$, with $G$ a (complex) semi-simple Lie group, it is very well-known that equivariant vector bundles $E$ over $B$ correspond to representations $(V_ …

(Work over complex numbers) Let $V$ be an orthogonal space. Let $Pin(V)$ be the double cover of the orthogonal group $O(V)$. Then $Pin(V)$ has a basic spin representation which we …

I am looking for literature that might contain the spherical representations of $GL(n, \mathbb{C})$. Here a spherical representation is an irreducible representation $\rho$ of $G$ …

I'm trying to understand the standard $GL(3,\mathbb{R})$ action on the 15-dimensional space of possible values for the derivative of the Riemann curvature tensor of a 3-dimensional …

A subgroup of $SL_2(\mathbb{R})$ is called arithmetic if it is commensurable with $SL_2(\mathbb{Z})$. An arithmetic subgroup is called congruence if it contains a subgroup of typ …

Let $G$ be a connected, simply-connected, complex semisimple Lie group with Lie algebra $\frak{g}$. Let $\mu:T^*\mathcal{B}\rightarrow\mathcal{N}$ be the Springer resolution of $\m …

Let $G_1, G_2$ be connected semisimple Lie groups, let us assume for simplicity that both groups are complex (even though, I am interested in the real Lie groups as well). Let $f: …

Is there a standard normal form for homogeneous cubic polynomials in $\mathbb{R}[x_1, x_2, x_3]$? Or, put another way, is there a nice way to describe the orbit space of the natur …

Wich representations of $F_{4}$, $E_{8}$ and $G_{2}$ are quasi-minuscule?

I am trying to read Harish-Chandra's book on automorphic forms on Semisimple Lie groups, and he keeps referring to Borel's Paris lecture notes. Does anyone have an online version o …

Does anyone have a link to a copy of Beilinson-Bernstein's "Localisation de g-modules", in which they prove the Beilinson-Bernstein theorem? I can't find it anywhere.

Let $\Delta$ be a Zariski dense finitely generated subgroup of $SL(3,\mathbb{R})$. Assume that $\Delta$ contains no element of finite order. Then, does there exist a finite-order …

Let $E=\mathfrak{so}(n,\mathbb{C})$ be the Lie algebra of antisymmetric complex matrices. We consider the action of the complex orthogonal group $SO(n,\mathbb{C})$ on $E$ by conjug …

Let $X$ be an affine algebraic variety over $\mathbb{C}$, and let $G$ be a semisimple complex linear algebraic group acting by variety automorphisms with finitely many orbits. The …

It is well-known that (left) $G$-invariant differential operators on a Lie group $G$, has an algebraic description, i.e. universal enveloping algebra of the Lie algebra of the grou …