Intermediate Wakimoto modules for Affine sl(n+1)

We construct certain boson type realizations of affine sl(n+1) that depend on a parameter r. When r=0 we get a Fock space realization of Imaginary Verma modules appearing in the work of the first author and when r=n they are the Wakimoto modules described in the work of Feigin and Frenkel

On Gelfand-Zetlin modules

summary:[For the entire collection see Zbl 0742.00067.]\par Let {\germ g}\sb k be the Lie algebra {\germ gl}(k,\mathcal{C}), and let U\sb k be the universal enveloping algebra for {\germ g}\sb k. Let Z\sb k be the center of U\sb k. The authors consider the chain of Lie algebras {\germ g}\sb n\supset {\germ g}\sb{n-1}\supset\dots\supset {\germ g}\sb 1. Then Z=\langle Z\sb k\mid k=1,2,\dots n\rangle is an associative algebra which is called the Gel'fand-Zetlin subalgebra of U\sb n. A {\germ g}\sb n module $V$ is called a $GZ$-module if V=\sum\sb x\oplus V(x), where the summation is over the space of characters of $Z$ and V(x)=\{v\in V\mid(a-x(a))\sp mv=0, m\in\mathcal{Z}\sb +, $a\in\mathcal{Z}\}$. 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

Dynkin diagrams and spectra of graphs

Dynkin diagrams rst appeared in [20] in the connection with classication of simple Lie groups. Among Dynkin diagrams a special role is played by the simply laced Dynkin diagrams An, Dn, E6, E7 and E8. Dynkin diagrams are closely related to Coxeter graphs that appeared in geometry (see [8]). After that Dynkin diagrams appeared in many braches of mathematics and beyond, em particular em representation theory

Virasoro action on Imaginary Verma modules and the operator form of the KZ-equation

We define the Virasoro algebra action on imaginary Verma modules for affine sl(2) and construct the analogs of Knizhnik-Zamolodchikov equation in the operator form. Both these results are based on a free field realization of imaginary Verma modules

Systems of subspaces of a unitary space

For a given poset, we consider its representations by systems of subspaces of a unitary space ordered by inclusion. We classify such systems for all posets for which an explicit classification is possible.Comment: 20 page