Intereting Posts

Show that an infinite set $C$ is equipotent to its cartesian product $C\times C$
Laplace transformations for dummies
$2^n=C_0+C_1+\dots+C_n$
Tensor products of functions generate dense subspace?
Is my proof valid? Integration of logarithmic function.
How many rationals of the form $\large \frac{2^n+1}{n^2}$ are integers?
If $n = m^3 – m$ for some integer $m$, then $n$ is a multiple of $6$
Probability and Laplace/Fourier transforms to solve limits/integrals from calculus.
Is $\mathbb{R}$ a finite field extension?
Linear Algebra: determine whether the sets span the same subspace
measurability with zero measure
Limit of the geometric sequence
Simplifying $\sum_{r = 0}^{n} {{n}\choose{r}}r^k(-1)^r$
How prove this $\sum_{k=1}^{2^{n-1}}\sigma{(2^n-2k+1)}\sigma{(2k-1)}=8^{n-1}$
Properties of the Mandelbrot set, accessible without knowledge of topology?

I have homework in a course on Lie groups, in which I must show that $(\pi_m,\mathbb C_m[x,y])$ are the only irreducible representations of finite dimension in SL(2,ℝ). Here $ C_m[x,y])$ is the vector space of homogeneous polynomials, and $\pi_m(g)$ acts via $\pi_m(g)(f(x,y))=f((x,y)\cdot g)$. It was not too complicated to calculate the characters, taking the basis $\{p_k:0\leq k \leq n\}$ with $p_k = x^ky^{n−k}$, since $\pi_m(exp(H))p_k=exp(d\pi_m(H))p_k=exp(2k−n)p_k$, but the question is how one could define an inner product for these matrices. But, I don’t have the volume form of SL(2,ℝ) to define the integral $\langle f,g \rangle=\int_Gf(z)⋅\overline{g(z)}dz$

- Use implicit function theorem to show $O(n)$ is a manifold
- Computing fundamental forms of implicit surface
- how to show $SU(2)/\mathbb{Z}_2\cong SO(3)$
- Gradient in differential geometry
- How to prove that every Lie group is the semidirect product of a connected Lie group and a discrete group?
- Control on Conformal map
- A general element of U(2)
- Is the determinant the “only” group homomorphism from $\mathrm{GL}_n(\mathbb R)$ to $\mathbb R^\times$?
- Is the infinitesimal generator for Lie groups the same as the infinitesimal generator of a Markov semigroup?
- Tensors as mutlilinear maps

- When asked to show that $X=Y$, is it reasonable to manipulate $X$ without thinking about $Y$?
- Cantor set as a set of continued fractions?
- Locally bounded Family
- An easy example of a non-constructive proof without an obvious “fix”?
- Can $S^0 \to S^n \to S^n$ become a fiber bundle when $n>1$?
- On the possible values of $\sum\varepsilon_na_n$, where $\varepsilon_n=\pm1$ (i.e., changing signs of the original series)
- Does associativity imply commutativity?
- Rearrangement of sequences with limit $0$
- Are Linear Transformations Always Second Order Tensors?
- If $X$ is a connected metric space, then a locally constant function $f: X \to $ M, $M $ a metric space, is constant
- Why is compactness in logic called compactness?
- Recursive Function – $f(n)=f(an)+f(bn)+n$
- Pointwise converging subsequence on countable set
- Every alternating permutation is a product of 3-cycles
- Right adjoints preserve limits