Timeline for Some question about polynomial representations of $GL(V)$
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| May 15, 2014 at 8:30 | vote | accept | Alex | ||
| May 14, 2014 at 16:46 | comment | added | Tom Church | This is just about the difference between "rational" and "polynomial". Let's consider $\text{GL}(1)$. The irreducible rational representations of $\text{GL}(1)=\mathbb{C}^\times$ (or $\mathbb{G}_m$) are indexed by integers $k\in \mathbb{Z}$, with $k\in \mathbb{Z}$ corresponding to the 1-dimensional representation on which $z\in \mathbb{C}^\times$ acts by $z^k$. This is a rational function of $z$, matching the terminology. But $z^k$ is only a polynomial when $k\geq 0$, so the irreducible polynomial representations are indexed by $k\geq 0\in \mathbb{Z}$. | |
| May 14, 2014 at 16:25 | comment | added | emiliocba | Proposition 1 in sciencedirect.com/science/article/pii/S0021869307004619 maybe helps you. | |
| May 14, 2014 at 16:11 | answer | added | Steven Sam | timeline score: 8 | |
| May 14, 2014 at 15:47 | history | asked | Alex | CC BY-SA 3.0 |