Abstracts

(* introductory talk series)

■*Yusuke Arike, Kagoshima

Title: Pseudo-trace functions

Abstract:

Pseudo-trace functions were introduced by Miyamoto in order to explain modular invariance property of characters of non-rational vertex operator algebras.

Pseudo-trace functions are originally defined in terms of symmetric linear forms on nth Zhu's algebras.

In this talk I will explain how to define pseudo-trace functions without $n$th Zhu's algebras, and construct pseudo-trace functions for several non-rational vertex operator algebras.

■*Scott Carnahan, Tsukuba

Title: Vertex algebras over commutative rings

Abstract: When Borcherds introduced vertex algebras in 1986, he defined them over any commutative ring. This direction of generality has received relatively little attention, because most applications, such as questions from physics, only use the field of complex numbers as a base ring. However, working over rings gives us some flexibility: we may do nontrivial gluing constructions, and draw concrete ties between zero and positive characteristic worlds.

■Thomas Creutzig, Alberta

Title: V^p-algebras

Abstract:

V^p-algebras are introduced as inverse quantum Hamiltonian reduction. They have nice structural properties that solve various conjectures from physics and representation theory. I will explain.

This is joint work with Adamovic, Genra and Yang.

■Chongying Dong, UC Sant Cruz, Sichuan

Title: Modular extension of fusion categories

Abstract: Give a rational, C_2-cofinite vertex operator algebra V and a finite automorphism automorphism group G, then V^G-submodules of V and V^G-submodules of V-modules generate two fusion categories. I will discuss the minimal modular extensions of these fusion categories. This is a research project in progress with Richard Ng and Li Ren.

■Zachary Fehily, Melbourne

Title: Relaxed highest-weight modules for Bershadsky-Polyakov algebras

Abstract: I will describe some of my recent progress in understanding the representation theory of the admissible-level Bershadsky-Polyakov algebras. In particular, a classification of relaxed highest-weight modules of these algebras will be presented. This result provides us with a class of non-rational W-algebras where representations, characters and modular transformations are within reach. These results will also assist in understanding the representations underlying the admissible-level WZW models associated with sl3.

■*Toshiro Kuwabara, Tsukuba

Title: quantization of toric hyperkahler varieties and its chiralization

Abstract:

In the classical Lie theory, quantization of conical symplectic singularities gives interesting

classes of noncommutative associative algebras, e.g. enveloping algebras of simple Lie

algebras, finite W-algebras and symplectic reflection algebras (rational Cherednik algebras).

In my talks, we discuss the construction of chiralization (vertex algebra analog) of such a

quantization in the case where the corresponding symplectic singularities are toric hyperkahler

varieties.

■Ching Hung Lam, Academia Sinica

Title: Automorphism groups of holomorphic VOAs of central charge 24

Abstract:

In this talk, we first describe the full automorphism group of certain

orbifold VOA $V_{\Lambda_g}^g$ associated with some coinvariant lattices

of the Leech lattice $\Lambda$. We will then use it to describe

the full automorphism groups of holomorphic VOAs of central charge 24.

■Tianshu Liu, Kyoto

Title: Correspondences among CFTs with different W-algebra symmetry

Abstract: Besides the well-studied W_N algebras, non-regular W-algebras are receiving increasing attention lately in both physics and mathematics. These are W-algebras associated with non-regular embeddings of sl(2) into Lie algebra g. In this talk, I will discuss a generalisation of the Ribault-Teschner relation and compute correlation functions of various non-regular W-algebras. This is only possible due to the fact that non-regular W-algebras admit to more than one free field realisations.

■Shigenori Nakatsuka, Tokyo

Title: New dualities in W-superalgebras

Abstract: The principal W-algebras enjoy Feigin-Frenkel duality and it has been an open problem to generalize it to the W-algebras associated with other nilpotent elements or to the W-superalgebras. In this talk, we will show that the Heisenberg cosets of the subregular W-algebras for $sl_{n+1}$ and $so_{2n+1}$ are isomorphic to Heisenberg cosets of the principal W-superalgebras for $sl_{1|n+1}$ and $osp_{2|2n}$ at the Feigin-Frenkel duality levels. Furthermore, we will show that these two pairs of vertex algebras are obtained from each other by taking Heisenberg cosets after tensoring with certain lattice vertex superalgebras. It resembles the Kazama-Suzuki coset construction and its inverse in the sense of R. Sato [arXiv:1907.02377]. This is a joint work with Thomas Creutzig and Naoki Genra.

■Li Ren, Sichuan

Title: Vertex operator superalgebras

Abstract: Let V = V_0 +V_1 be a vertex operator superalgebra. Then V has a canonical automorphism \sigma of order 2 from the super structure. We assume V is rational and C2-cofinite. We will discuss the super \sigma-twisted modules,connection between representations of V and V_0 . We will also explain how the representation theory of V is related to the 16-fold way conjecture in category theory. This talk is based on joint work with Chongying Dong and Richard Ng.

■David Ridout, Melbourne

Title: Quantum hamiltonian reduction --- beyond category O.

Abstract:

Quantum hamiltonian reduction relates affine VOAs to

W-algebras and provides functors between their module categories. There

is a lot known about these functors when the source is category O for

the affine VOA. However, it has been known for a long time that this

category is too small for applications to conformal field theory. I

will discuss some computations, joint with Steve Siu, that extend

quantum hamiltonian reduction to the category of all weight modules over

L_k(sl_2), for k admissible.

■Hiroki Shimakura, Tohoku

Title: On inertia groups and uniqueness of holomorphic vertex operator algebras of central charge 24

Abstract:

I talk about the inertia group of a holomorphic vertex

operator algebra, which consists of all automorphisms acting on the

weight one subspace trivially. As an application, I discuss the

uniqueness of some holomorphic vertex operator algebras of central

charge 24.

■Kenichiro Tanabe, Hokkaido

Title: The irreducible weak modules for the fixed point subalgebra of the vertex algebra associated to a non-degenerate even lattice by an automorphism of order $2$

Abstract:

Let $V_{L}$ be the vertex algebra associated to a non-degenerate even lattice $L$,

$\theta$ the automorphism of $V_{L}$ induced from the $-1$ symmetry of $L$, and

$V_{L}^{+}$ the fixed point subalgebra of $V_{L}$ under the action of $\theta$.

When $L$ is positive definite, the classification of irreducible $V_{L}^{+}$-modules is obtained by

Dong--Nagatomo in the case that the rank of $L$ is $1$

and by Abe--Dong in the general case.

We classify the irreducible weak $V_{L}^{+}$-modules for an arbitrary non-degenerate even lattice $L$.

■Mamoru Ueda, Kyoto

Title: Affine Super Yangians and Rectangular $W$-superalgebras

Abstract:

Ragoucy and Sorba have constructed surjective homomorphisms from finite

Yangians of type $A$ to rectangular $W$-algebras of type $A$. In this

talk, we explain the corresponding result in the affine super setting.

First, we define the affine super Yangian which is the deformation of the

current algebra $\widehat{\mathfrak{gl}}(m,n)\otimes\mathbb{C}[u]$ and

give the minimalistic presentation of it. Next, we construct the

generators of rectangular $W$-superalgebras of type $A$. Finally, we give

surjective homomorphisms from the affine super Yangian to universal

enveloping algebras of rectangular $W$-superalgebras of type $A$.

■Takahiro Yabe, Tokyo

Title: On the classification of 2-generated axial algebras of Majorana type with flips

Abstract:

The classification of algebras generated by 2-Ising vectors was proved by S.\ Sakuma in 2007 and the classification of 2-generated Majorana algebras was proved by A.\ A.\ Ivanov et.\ al. in 2010.

In this talk, I will generalise these results by using a class of axial algebras which I call axial algebras of Majorana type with flips.

■Hiromichi Yamada, Hitotsubashi

Title: Vertex operator algebras associated with $\mathbb{Z}_{2k}$-codes

Abstract:

We first consider a simple, self-dual, rational, and $C_2$-cofinite

vertex operator algebra $U$ of CFT-type whose simple current modules

are graded by $\mathbb{Z}_{2k}$.

Using those simple current modules, we construct

a vertex operator algebra $U_D$ associated with a $\mathbb{Z}_{2k}$-code $D$.

We classify the irreducible $U_D$-modules.

All the irreducible modules are realized

in a module for a certain lattice vertex operator algebra.

This is a joint work with Hiroshi Yamauchi.

■Hiroshi Yamauchi, Tokyo Women Cristian

Title: A c=33 extremal VOA

Abstract:

Tener-Wang formulated a notion of non-holomorphic extremal VOAs and

Grady-Tener extensively studied and almost classified extremal VOAs of rank 2.

In this talk I will explain a construction of c=33 extremal VOA of

rank 2, which was the last piece of their classification.

This result is based on a joint work with Ching Hung Lam.