Tagged Questions
2
votes
1answer
81 views
elementary but confounding question about integer matrices (related to hecke operators)
Let $\Gamma(N)$ denote the kernel of the reduction map $\text{SL}_2(\mathbb{Z})\rightarrow\text{SL}_2(\mathbb{Z}/N\mathbb{Z})$
Let $p$ be a prime that is $1$ mod $N$, and let $M$ be the set of ...
1
vote
2answers
130 views
Is there some kind of character theory for representations of finite dimensional algebras?
We know that for a representation $V$ of a Lie algebra or a quantum group, we can define character of $V$ as $ch(V)=\sum_{\mu} dim(V_{\mu})e^{\mu}$, where $V_{\mu}$ is the weight space of $V$ with ...
5
votes
0answers
95 views
Tensor product decomposion in Lie algebras
As a chemist, I do this all the time...for symmetry groups. Which are finite, luckily :-)
For knot theory purposes, I'd like to have a complete list of Lie group irreps R with
the property that the ...
0
votes
1answer
100 views
Compare of coefficients of two formal power series
Define $$ \Lambda_{i}(u) = \sum_{r=0}^{\infty} \Lambda_{i,r}u^{r}, \Psi_{i}(u) = \sum_{m=0}^{\infty} \psi_{i,m}u^{m}=k_i\frac{\Lambda_{i}(uq_i^{-1})}{\Lambda_{i}(uq_i)}. $$ How can we show that $$ ...
1
vote
1answer
80 views
questions about the paper: Affine quivers and canonical bases
I am reading the paper Affine quivers and canonical bases. I have a question on page 114 of the paper. In the proof of property (b), line 6 of page 114, why "for each $\gamma \neq 1$, $tr(\gamma, ...
3
votes
1answer
100 views
How to compute the Gel'fand Models for a (quantum) Lie Algebra
Given a lie algebra $g$, how does one approach finding the Gel'fand models? For clarity, by this I mean
$\bigoplus_{\lambda\in P^+}V(\lambda)$ where $P^+$ are the dominant weights, and ...
