Timeline for Mistake in Discriminants, Resultants, and Multidimensional Determinants?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 31, 2018 at 17:26 | comment | added | S. carmeli | This is not a mistake, in this book they consider algebraic geometry, and hence consider only \textbf{polynomial} (i.e. regular) functions. The complex conjugate of a polynomial function is anti-holomorphic and hence not a "function" in Gelfand-Kapranov-Zelevinski context. | |
| Mar 30, 2018 at 22:44 | comment | added | LSpice | I'm sure it goes back much earlier than that, but a natural source for polynomial representations of $\mathrm{GL}(n)$ (the 1-dimensional ones being those @NeilStrickland describes) is Green - Polynomial representations of $\mathrm{GL}(n)$. | |
| Mar 30, 2018 at 20:59 | comment | added | Vincenzo Zaccaro | @NeilStrickland many thanks for the helpfull remark. Can you give me a rference where I can find your claim? I know almost nothing about Rep. Theory. | |
| Mar 30, 2018 at 20:31 | comment | added | Adam P. Goucher | A more pathological multiplicative function is $\chi(g) = \exp f(\log |\det g|)$, where $f$ is any solution to Cauchy's functional equation, and we further define $\chi(g) = 0$ whenever $g$ is singular. | |
| Mar 30, 2018 at 20:15 | comment | added | Neil Strickland | The function $f$ is polynomial, and we can fix a generic $M$ and define $\chi(g)=f(gM)f(M)^{-1}$, so $\chi$ is also a polynomial function. Any character that is a polynomial function is a power of the determinant. | |
| Mar 30, 2018 at 20:05 | history | asked | Vincenzo Zaccaro | CC BY-SA 3.0 |