An explicit realization of logarithmic modules for the vertex operator algebra W_{p,p'}

By extending the methods used in our earlier work, in this paper, we present an explicit realization of logarithmic \mathcal{W}_{p,p'}-modules that have L(0) nilpotent rank three. This was achieved by combining the techniques developed in \cite{AdM-2009} with the theory of local systems of vertex operators \cite{LL}. In addition, we also construct a new type of extension of $\mathcal{W}_{p,p'}$, denoted by $\mathcal{V}$. Our results confirm several claims in the physics literature regarding the structure of projective covers of certain irreducible representations in the principal block. This approach can be applied to other models defined via a pair screenings.Comment: 18 pages, v2: one reference added, other minor change

On coset vertex algebras with central charge 1

We present a coset realization of the vertex operator algebra $V_L ^+$ with central charge $1$. We investigate the vertex operator algebra $V_{Z sqrt{2n}} ^+$ (resp. $V_{2Z sqrt{2n+1}} ^+$) as a vertex subalgebra of $L_{D_n ^{(1)}}(Lambda _0) otimes L_{D_n ^{(1)}}(Lambda _0)$ (resp. $L_{B_n ^{(1)}}(Lambda _0) otimes L_{B_n ^{(1)}}(Lambda _0)$). Our construction is based on the boson-fermion correspondence and certain conformal embeddings

Representations of certain non-rational vertex operator algebras of affine type

In this paper we study a series of vertex operator algebras of integer level associated to the affine Lie algebra $A_{\ell}^{(1)}$. These vertex operator algebras are constructed by using the explicit construction of certain singular vectors in the universal affine vertex operator algebra $N(n-2,0)$ at the integer level. In the case $n=1$ or $l=2$, we explicitly determine Zhu's algebras and classify all irreducible modules in the category $\mathcal{O}$. In the case $l=2$, we show that the vertex operator algebra $N(n-2,0)$ contains two linearly independent singular vectors of the same conformal weight.Comment: 15 pages, LaTeX; final version, to appear in J. Algebr

Fusion rules and complete reducibility of certain modules for affine Lie algebras

We develop a new method for obtaining branching rules for affine Kac-Moody Lie algebras at negative integer levels. This method uses fusion rules for vertex operator algebras of affine type. We prove that an infinite family of ordinary modules for affine vertex algebra of type A investigated in Adamovi\'c and O. Per\v{s}e (2008) is closed under fusion. Then we apply these fusion rules on explicit bosonic realization of level -1 modules for the affine Lie algebra of type $A_{\ell-1}^{(1)}$, obtain a new proof of complete reducibility for these representations, and the corresponding decomposition for $\ell \ge 3$. We also obtain the complete reducibility of the associated level -1 modules for affine Lie algebra of type $C_{\ell}^{(1)}$. Next we notice that the category of $D_{2 \ell -1}^{(1)}$ modules at level $- 2 \ell +3$ obtained in Per\v{s}e (2012) has the isomorphic fusion algebra. This enables us to decompose certain $E_6 ^{(1)}$ and $F_4 ^{(1)}$--modules at negative levels.Comment: 18 pages; final version, to appear in Journal of Algebra and Its Application

Defining relations for minimal unitary quantum affine W-algebras

We prove that any unitary highest weight module over a universal minimal quantum affine $W$-algebra at non-critical level descends to its simple quotient. We find the defining relations of the unitary simple minimal quantum affine $W$-algebras and the list of all their irreducible positive energy modules. We also classify all irreducible highest weight modules for the simple affine vertex algebras in the cases when the associated simple minimal $W$-algebra is unitary.Comment: Latex file, 24 pages, revised versio

Water for all : Proceedings of the 7th international scientific and professional conference Water for all

The 7th International Scientific and Professional Conference Water for all is organized to honour the World Water Day by the Josip Juraj Strossmayer University of Osijek, European Hygienic Engineering & Design Group (EHEDG), Danube Parks, Croatian Food Agency, Croatian Water, Faculty of Food Technology Osijek, Faculty of Agriculture in Osijek, Faculty of Civil Engineering Osijek, Josip Juraj Strossmayer University of Osijek Department of Biology, Josip Juraj Strossmayer University of Osijek Department of Chemistry, Nature Park “Kopački rit”, Osijek- Baranja County, Public Health Institute of the Osijek- Baranja County and „Vodovod-Osijek“ -water supply company in Osijek. The topic of World Water Day 2017 was "Wastewater" emphasizing the importance and influence of wastewater treatments on global environment. The international scientific and professional conference Water for all is a gathering of scientists and experts in the field of water management, including chemists, biologists, civil and agriculture engineers, with a goal to remind people about the significance of fresh water and to promote an interdisciplinary approach and sustainability for fresh water resource management. The Conference has been held since 2011. About 300 scientists and engineers submitted 95 abstracts to the 7th International Scientific and Professional Conference Water for all, out of which 33 was presented orally and 62 as posters. 47 full papers were accepted by the Scientific Committee. 38 full papers became the part of the this Proceedings while 9 papers were accepted for publication in Croatian Journal of Food Science and Technology and Electronic Journal of the Faculty of Civil Engineering Osijek - e-GFOS

Vertex Algebra Approach to Fusion Rules for N=2 Superconformal Minimal Models

AbstractLet Lcm be the vertex operator superalgebra associated to the unitary vacuum module for the N=2 superconformal algebra with the central charge cm=3mm+2,m∈N. Then the unitary N=2-modules give all irreducible modules for the vertex operator superalgebra Lcm. In this paper, we determine all fusion rules for Lcm-modules from the vertex algebra point of view. These fusion rules coincide with the fusion rules obtained by M. Wakimoto (Fusion rules for N=2 superconformal modules, hep-th/9807144) using a modified Verlinde formula