## Algebarske i kombinatorne metode u teoriji verteks algebri

**Opis projekta**

In the proposed project we shall study the representation theory of important classes of vertex algebras with particular emphasis on the theory of vertex algebras with origins in physics. We shall also study the affine vertex algebras and their connections with W-algebras. Based on previous research of D. Adamović and O. Perše from the papers J. Algebra 319 (2008); SIGMA 8 (2012); Algebras and Representation Theory 16 (2013) we shall apply the representation theory of vertex algebras of affine type to the structure and representation theory of W-algebras. In the last few years, C2-cofinite, irrational vertex algebras with non-semisimple representation categories attracted a lot of interest. Such vertex algebras also appear in the logarithmic conformal field theory. By using methods developed in the papers by D. Adamović and A. Milas: Adv. Math. 217 (2008), Comm. Math. Phys. 288 (2009), Adv. Math. 227 (2011) and J. Math. Phys. 73511 (2012) we shall study the representation theory of certain irrational, C2-cofinite vertex algebras and their connections with the theory of quantum groups. An emphasis will be put on the tensor categories of modules of C2-cofinite vertex algebras, the determination of fusion rules, orbifold vertex subalgebras and the explicit realization of logarithmic representations. A part of the research will be devoted to some combinatorial aspects of the representation theory of affine Kac-Moody Lie algebras. We will study the application of intertwining operators on the determination of combinatorial bases of Feigin-Stoyanovsky type subspace and the associated fermionic character formulas developed by M. Primc and collaborators. We also plan to apply the above methods on the combinatorial structures related to triplet vertex algebras and logarithmic CFT.

**Akronim**

ACMVAT

**Šifra projekta**

IP-2013-11-2634

**Poziv**

2013-11

**Financijer**

HRZZ - Hrvatska zaklada za znanost

**Linija financiranja**

IP - Research Projects

**Nadležnost**

Hrvatska

**Ukupan iznos financiranja projekta**

546.420,00 HRK

**Trajanje projekta**

2014-07-01 - 2018-06-30

**Ustanova - uloga**

Prirodoslovno-matematički fakultet, Zagreb -

**Osoba - uloga**

Dražen Adamović - Voditelj projekta