Two Problems on Cartan Domains
| dc.creator | Yin, Weiping | |
| dc.date | 2006-03-09 | |
| dc.date.accessioned | 2026-07-07T07:06:41Z | |
| dc.date.available | 2026-07-07T07:06:41Z | |
| dc.description | Firstly, we consider the unitary geometry of two exceptional Cartan domains $\Re_{V}(16)$ and $\Re_{VI}(27)$. We obtain the explicit formulas of Bergman kernal funtion, Cauchy-Szegö kernel, Poinsson kernel and Bergman metric for $\Re_{V}(16)$ and $\Re_{VI}(27)$. Secondly, we give a class of invariant differential operators for Cartan domain $\Re$ of dimension n: If the Bergman metric of $\Re$ is $$ds^{2}=\sum\limits_{i,j=1}^{n}g_{ij}dz_{i}d\bar{z}_{j}, T(z,\bar{z})=(g_{ij})$$ and $$L(u)=T^{-1}(z,\bar{z}) [\frac{\partial^2u}{\partial z_i\partial\bar{z}_j}],$$then $$L_j(u)=\{\mbox {The sum of all prinipal minors of degree} j {for} L(u)\}$$ is invariant under the biholomorphic mapping of $\Re$. Let $D$ be the irreducible bounded homogeneous domain in $C^n$, $P=P(z,*)$ the Poisson kernel of $D$, then for any fixed $J(1\leq j \leq n)$ one has $L_j(P^{1/j})=0$ iff $D$ is a symmetric domain. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0603205 | |
| dc.identifier | http://arxiv.org/abs/math/0603205 | |
| dc.identifier | J. of China Univ. of Sci. and Tech., 1986, 16(2): 130-146 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110114 | |
| dc.subject | Complex Variables | |
| dc.subject | 32A07 | |
| dc.title | Two Problems on Cartan Domains | |
| dc.type | text |