5
votes
1answer
253 views

Equivalence of exterior forms

Let us start with the following definition. Let $1\leqslant k\leqslant n$ and let $\omega_1,\omega_2\in\Lambda^k(\mathbb{R}^n)$. We say that $\omega_1$, $\omega_2$ are equivalent, if there exists ...
5
votes
1answer
112 views

Are SL(n) Invariants of this wedge product isomorphic to a symmetric product?

In the course of investigating a conjecture about a "strange duality" for sections of line bundles on various models of moduli of sheaves on $\mathbb P^2$, another student and I reduced one special ...
1
vote
0answers
152 views

Non-negative Quadratic forms with Exterior Forms

Hello All, I apologize if the following question is too elementary. Any suggestion is greatly appreciated. Thank you. Let $n\geqslant 4$, $X$ be an $n$-dimensional inner product space over ...
0
votes
1answer
238 views

Inequalities Involving Wedge Product (Reference Request)

Hello, I'm looking for references on various inequalities involving the wedge product and exterior forms. The only references I could hunt down are references on Hadamard-Schwarz Inequality. The ...
3
votes
1answer
179 views

Decomposability of exterior two-forms

Hello, The following question appears as a step in my proof. It seems easy but somehow I have not been able to prove this. I could solve few special cases though. Any help in this context is ...
4
votes
3answers
2k views

n-dimensional “cross product” reference request

I have written a paper which involves a "cross product" in $\mathbb{R}^n$ and I would like to have a reference to point to. Let ${\bf e_1}, \dots, {\bf e_n}$ be the standard basis for $\mathbb{R}^n$ ...