Drinfeld Zastava is a certain closure of the moduli space of maps from the projective line to the Kashiwara flag scheme of the affine Lie algebra ${\widehat{\mathrm{𝔰𝔩}}}_n$. We introduce an affine, reduced, irreducible, normal quiver variety $Z$ which maps to the Zastava space bijectively at the level of complex points. The natural Poisson structure on the Zastava space can be described on $Z$ in terms of Hamiltonian reduction of a certain Poisson subvariety of the dual space of a (nonsemisimple) Lie algebra. The quantum Hamiltonian...

We construct new monomial quasi-particle bases of Feigin-Stoyanovsky type subspaces for the affine Lie algebra sl(3;ℂ)∧ from which the known fermionic-type formulas for (k, 3)-admissible configurations follow naturally. In the proof we use vertex operator algebra relations for standard modules and coefficients of intertwining operators.

Given a tuple $({𝒳}_1,...,{𝒳}_k)$ of irreducible characters of $G{L}_n\left(F_q\right)$ we define a star-shaped quiver $\Gamma$ together with a dimension vector $v$. Assume that $({𝒳}_1,...,{𝒳}_k)$ is generic. Our first result is a formula which expresses the multiplicity of the trivial character in the tensor product ${𝒳}_1\otimes \cdots \otimes {𝒳}_k$ as the trace of the action of some Weyl group on the intersection cohomology of some (non-affine) quiver varieties associated to $(\Gamma ,v)$. The existence of such a quiver variety is subject to some condition. Assuming that this condition is satisfied, we...