On Gelfand-Zetlin modules

Drozd, Yu. A., Ovsienko, S. A., and Futorny, V. M.. "On Gelfand-Zetlin modules." Proceedings of the Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 1991. [143]-147. <http://eudml.org/doc/220503>.

@inProceedings{Drozd1991,
abstract = {[For the entire collection see Zbl 0742.00067.]Let $\{\mathfrak \{g\}\}_k$ be the Lie algebra $\{\mathfrak \{g\}l\}(k,\mathcal \{C\})$, and let $U_k$ be the universal enveloping algebra for $\{\mathfrak \{g\}\}_k$. Let $Z_k$ be the center of $U_k$. The authors consider the chain of Lie algebras $\{\mathfrak \{g\}\}_n\supset \{\mathfrak \{g\}\}_\{n-1\}\supset \dots \supset \{\mathfrak \{g\}\}_1$. Then $Z=\langle Z_k\mid k=1,2,\dots n\rangle $ is an associative algebra which is called the Gel’fand-Zetlin subalgebra of $U_n$. A $\{\mathfrak \{g\}\}_n$ module $V$ is called a $GZ$-module if $V=\sum _x\oplus V(x)$, where the summation is over the space of characters of $Z$ and $V(x)=\lbrace v\in V\mid (a-x(a))^mv=0$, $m\in \mathcal \{Z\}_+$, $a\in \mathcal \{Z\}\rbrace $. The authors describe several properties of $GZ$- modules. For example, they prove that if $V(x)=0$ for some $x$ and the module $V$ is simple, then $V$ is a $GZ$-module. Indecomposable $GZ$- modules are also described. The authors give three conjectures on $GZ$- modules and!},
author = {Drozd, Yu. A., Ovsienko, S. A., Futorny, V. M.},
booktitle = {Proceedings of the Winter School "Geometry and Physics"},
keywords = {Srni (Czechoslovakia); Proceedings; Winter school; Geometry; Physics},
location = {Palermo},
pages = {[143]-147},
publisher = {Circolo Matematico di Palermo},
title = {On Gelfand-Zetlin modules},
url = {http://eudml.org/doc/220503},
year = {1991},
}

TY - CLSWK
AU - Drozd, Yu. A.
AU - Ovsienko, S. A.
AU - Futorny, V. M.
TI - On Gelfand-Zetlin modules
T2 - Proceedings of the Winter School "Geometry and Physics"
PY - 1991
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [143]
EP - 147
AB - [For the entire collection see Zbl 0742.00067.]Let ${\mathfrak {g}}_k$ be the Lie algebra ${\mathfrak {g}l}(k,\mathcal {C})$, and let $U_k$ be the universal enveloping algebra for ${\mathfrak {g}}_k$. Let $Z_k$ be the center of $U_k$. The authors consider the chain of Lie algebras ${\mathfrak {g}}_n\supset {\mathfrak {g}}_{n-1}\supset \dots \supset {\mathfrak {g}}_1$. Then $Z=\langle Z_k\mid k=1,2,\dots n\rangle $ is an associative algebra which is called the Gel’fand-Zetlin subalgebra of $U_n$. A ${\mathfrak {g}}_n$ module $V$ is called a $GZ$-module if $V=\sum _x\oplus V(x)$, where the summation is over the space of characters of $Z$ and $V(x)=\lbrace v\in V\mid (a-x(a))^mv=0$, $m\in \mathcal {Z}_+$, $a\in \mathcal {Z}\rbrace $. The authors describe several properties of $GZ$- modules. For example, they prove that if $V(x)=0$ for some $x$ and the module $V$ is simple, then $V$ is a $GZ$-module. Indecomposable $GZ$- modules are also described. The authors give three conjectures on $GZ$- modules and!
KW - Srni (Czechoslovakia); Proceedings; Winter school; Geometry; Physics
UR - http://eudml.org/doc/220503
ER -