Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Suppose $V$ is a finite dimensional complex vector space and $f:V\to V$ is an automorphism. There is a natural extension $\Lambda^\bullet(f):\Lambda^\bullet(V)\to\Lambda^\bullet(V)$ to the exterior algebra $\Lambda^\bullet(V)$. If $f$ is of finite order, one can use the anti-commutative version of Molien's formula to compute the Hilbert series $f(t)$ of the fixed subalgebra $\Lambda^\bullet(V)^{\Lambda^\bullet(f)}$: if $G$ is the group generated by $f$, then $$f(t) = \frac{1}{|G|} \sum_{g\in G}\det(1+t g).$$

Is there a variation of this for $f$ not of finite order?

share|cite|improve this question
1  
The obvious guess (replace this sum with a limit) fails; it doesn't distinguish the identity from the identity plus a nilpotent. I think you need some conditions on $f$. – Qiaochu Yuan Jul 12 '12 at 3:18

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.