On relaxed and logarithmic modules for affine vertex algebras

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:Dražen Adamović(克罗地亚萨格勒布大学)
:2022-06-29 15:00

报告人:Dražen Adamović(克罗地亚萨格勒布大学)

时  间:629日下午15:00

地  点:腾讯会议ID251-574-339(无密码)


We will first review certain general methods for constructing logarithmic (projective) modules. Then we will show how these methods can be applied on affine vertex algebras by using recent free field realizations, which are motivated by finding inverses of the Quantum Hamiltonian Reductions. A particular emphasis will be put on the realization of the affine vertex algebra $L_k(sl(3))$ as a subalgebra of $BP_k \otimes \mathcal S \otimes \Pi(0)$ where $BP_k$ is the Breshadsky-Polykov   algebra, $\mathcal S$ the $\beta-\gamma$ system   and $\Pi(0)$ is a half-lattice vertex algebra. We present a realization of logarithmic modules for $BP_k$ and logarithmic $L_k(sl_3)$ at (almost) arbitrary non-integral level k. Next we analyse the relaxed modules for $L_k(sl_3)$  with finite-dimensional and infinite-dimensional weight spaces. Finally, we discuss an affine analogs of the Feigin-Semikhatov algebra $W_{A_2}(p)$ and possible applications in a construction on new tensor categories and fusion rules. This talk is based on a recent joint work with T. Creutzig and N. Genra.


Dražen Adamović克罗地亚萨格勒布大学教授,研究领域为无穷维李代数、顶点算子代数及共形场论。研究成果发表在Adv. Math.Comm. Math. Phys.Selecta Math.等杂志。