0
votes
0answers
32 views
Differences of Numbers of Helicity States in 4-dimensional Strings
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 …
0
votes
0answers
24 views
non-locally simple $\mathcal{g}$-modules
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 …
3
votes
1answer
81 views
Orbit structure of linear representations of complex Lie groups
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 …
2
votes
2answers
199 views
Why is the equivariant Euler class a character ?
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 …
0
votes
1answer
66 views
Does the nonvanishing of a Littlewood-Richardson coefficient implies comparability of highest weights?
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 …
8
votes
1answer
791 views
What is Kirillov’s method good for?
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 …
2
votes
2answers
243 views
Equivariant Cohomology of a Complex Projective Variety
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 …
9
votes
2answers
260 views
Uncertainty principle on finite groups
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, …
5
votes
1answer
122 views
Does every equivalence class of Hecke characters contain a distinguished element?
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 …
3
votes
1answer
129 views
Subgroups of algebraic groups
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 …
4
votes
2answers
204 views
Are all representations of $G\times H$ induced from representations of $G$ and $H$?
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
…
7
votes
1answer
259 views
Who is the commutator sheaf?
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 …
1
vote
1answer
73 views
fixed vector of a generic representation of GL(n,F)
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 …
4
votes
1answer
137 views
Quantum 9j symbols?
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 …
7
votes
0answers
88 views
When is Ext*(M,N) finitely generated as a Ext*(M,M) module?
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 $ …

