4
votes
1answer
110 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 ...
5
votes
0answers
119 views

Is there an analogue of spin/oscillator representation for the general linear Lie algebra?

(Work over complex numbers) Let $V$ be an orthogonal space. Let $Pin(V)$ be the double cover of the orthogonal group $O(V)$. Then $Pin(V)$ has a basic spin representation which we can think of as the ...
7
votes
1answer
272 views

Question about decomposition of exterior product

In their paper "New lower bounds for the border rank of matrix multiplication", Landsberg and Ottaviani make use of the fact that $$\tag{$\dagger$} {\textstyle\bigwedge}^p(V\otimes W) \cong ...