The question whether the states in $D=2m + 2$ dimensional string theory, which carry a representation of $SO(2m)$, span spaces which carry representations of $SO(2m+1)$ seems hopel …

I'm interested in an example of a simple $\mathcal{g}$-module $M$ over some locally simple Lie algebra say $\mathcal{g}\simeq gl(\infty)$ such that $M$ is not isomorphic to a direc …

Let $G$ be a semisimple complex Lie group (or perhaps a reductive algebraic group over $\mathbb{C}$) and $V$ an irreducible finite-dimensional representation of $G$, determined by …

Let us first precise the question : let $T$ be a torus, $\alpha : T \to \mathbb{C}$ be an irreducible character. I am interested in the $T$-equivariant Euler class of the ($T$-equi …

Let $\mathfrak{g}$ be a semi-simple finite dimensional Lie algebra. Denote by $L(\lambda)$ an irreducible finite-dimensional $\mathfrak{g}$-module of highest weight $\lambda$. (I.e …

I am planing to study Kirillov's orbit method. I have seen Kirillov's method in several branch of mathematics, for instance, functional analysis, geometry, .... Why is this theory …

Suppose that I have a complex projective variety $X$ endowed with an algebraic action of a complex torus $T$. Suppose also that the set $X^T$ of fixed points is finite. I would lik …

For a finite group $G$ with normal subgroup $H$, the induced representation $\text{Ind}_H^G(1)$ decomposes as a sum of irreducibles with the multiplicities equal to the dimensions, …

Let $k$ be a number field and let $I_k$ denote the idele group of $k$. Let $$|\cdot|: (x_v) \mapsto \prod_{v \in \Omega_k} |x_v|,$$ denote the adelic norm map. If $I_k^1$ denotes …

Is anyone aware of a result (or a counterexample) along the following lines: let $G$ be an algebraic group over $\mathbf Z$. Let $H$ be a finite group such that $H$ occurs as a su …

This is a crosspost from math.SE. Suppose $G$ and $H$ are discrete groups. Is it always the case that any finite dimensional complex representation of $G\times H$ is of the form …

Let $G$ be a reductive algebraic group (say $GL_n$) and $[\cdot,\cdot]: G \times G \to G$ the commutator map taking $(g,h) \mapsto ghg^{-1} h^{-1}$. Note that $[\cdot,\cdot]$ and …

Hello, Let $F$ a localy compact non-archimidian field and $G_{n}$ the localy profinite group $GL(n,F)$. Let $\Gamma_{n,k}$ the subgroup of $G_{n}$ whose elements are the matrices …

A formula for (SU2) quantum 6j symbols exists. A formula expressing ordinary (q=1) 9j symbols in terms of 6j symbols is long known. Unfortunately, combining both (I tried it myself …

Let A be a finite dimensional algebra over a field k and M,N a finitely generated A-module. Im searching for examples where the module $ Ext^{o} (M,N) $ is a finitely generated $ …