Conveners
Algebra
- Slaven Kozic
Algebra
- Ivana Vukorepa
M.Primc and T.Šikić have described a combinatorial spanning set for a standard module for the affine Lie algebra of the type $C_\ell^{(1)}$ and have conjectured that this set is linearly independent. We will prove linear independence for certain classes of these modules by establishing a connection with combinatorial bases of Feigin-Stoyanovsky's type subspace of standard modules for the...
We present some results on the double Yangian associated with the Lie superalgebra $\mathfrak{gl}_{m|n}$. We establish the Poincaré-Birkhoff-Witt Theorem for the double Yangian. Then, we construct the dual counterpart of the quantum contraction for the dual Yangian and we show that its coefficients are central elements. As an application, we introduce reflection algebras, certain left coideal...
We consider W-algebras, a class of vertex algebras that non-linearly generalize the affine Kac-Moody Lie algebras and the Virasoro Lie algebra. They are obtained from the affine Kac-Moody Lie algebras through quantum Hamiltonian reductions parameterized nilpotent orbits. In this talk, we discuss how W-algebras are related to each other, which is partially anticipated from their connections to...
In this talk, we will discuss a concept of deformation of quantum vertex algebra module by braiding. Furthermore, we will present its applications to Yangians, their generalizations and reflection algebras. This is a joint work with Lucia Bagnoli.
In 1971., Steven J. Takiff, while studying invariant polynomial rings, defined a specific extension of the finite-dimensional Lie algebra. In his honor, mathematicians call the corresponding extensions of finite-dimensional simple Lie algebras, but also of some infinite-dimensional Lie algebras, Takiff algebras. Takiff algebras are also known as truncated current Lie algebras or *polynomial...
We investigate the representation theory of simple affine vertex algebra $L_k(\mathfrak{g})$ at special non-admissible levels $k_n=-\frac{2n+1}{2}$ for $\mathfrak{g} = \mathfrak{sl}_{2n}$. We classify irreducible $L_{k_n}(\mathfrak{sl}_{2n})$-modules in category $KL_{k_n}(\mathfrak{sl}_{2n})$ and prove that $KL_{k_n}(\mathfrak{sl}_{2n})$ is a semi-simple, rigid braided tensor category.
In...
