Related papers: Minimal model fusion rules from 2-groups
We find a nonsemisimple fusion algebra F_p associated with each (1,p) Virasoro model. We present a nonsemisimple generalization of the Verlinde formula which allows us to derive F_p from modular transformations of characters.
Let $n,q,t,s,p$ be non-negative integers where $n\geq s$ and $q\geq 1$. For $\mathbf{x}\in A_{q}^{n}\triangleq\{ 0,1,\ldots,q-1 \}^{n}$, let the $t$-insertion $s$-deletion $p$-substitution ball of $\mathbf{x}$, denoted by…
A $G$-graded extension of a fusion category $\mathcal{C}$ yields a categorical action of $G$ on the center $Z(\mathcal C)$. If the extension admits a spherical structure, we provide a method for recovering its fusion rules in terms of the…
We analyse the fusion products of certain representations of the Virasoro algebra for c=-2 and c=-7 which are not completely reducible. We introduce a new algorithm which allows us to study the fusion product level by level, and we use this…
Following a recent proposal of Richard Borcherds to regard fusion as the ring-like tensor product of modules of a {\em quantum ring}, a generalization of rings and vertex operators, we define fusion as a certain quotient of the (vector…
We give a construction and algorithmic description of the fusion ring of permutation extensions of an arbitrary modular tensor category using a combinatorial approach inspired by the physics of anyons and symmetry defects in bosonic…
It is shown that a particular $q$-deformation of the Virasoro algebra can be interpreted in terms of the $q$-local field $\Phi (x)$ and the Schwinger-like point-splitted Virasoro currents, quadratic in $\Phi (x)$. The $q$-deformed Virasoro…
Let $V$ be a simple vertex operator algebra, and $G$ a finite automorphism group of $V$ such that $V^G$ is regular. The definition of entries in $S$-matrix on $V^G$ is discussed, and then is extended. The set of $V^G$-modules can be…
We find the fusion rules for the quantum analogues of the complex reflection groups $H_n^s=\mathbb Z_s\wr S_n$. The irreducible representations can be indexed by the elements of the free monoid $\mathbb N^{*s}$, and their tensor products…
Suppose that $A$, $B$ and $S$ are non-empty subsets of a finite abelian group $G$. Then the generalized restricted sumset $$ A\stackrel{S}+B:=\{a+b:\,a\in A,\ b\in B,\ a-b\not\in S\} $$ contains at least $$ \min\{|A|+|B|-3|S|,p(G)\} $$…
The PQ mechanism resolving the strong CP problem and the seesaw mechanism explaining the smallness of neutrino masses may be related in a way that the PQ symmetry breaking scale and the seesaw scale arise from a common origin. Depending on…
A string field theory of (p,q) minimal superstrings is constructed with the free-fermion realization of 2-component KP (2cKP) hierarchy, starting from 2-cut ansatz of two-matrix models. Differential operators of 2cKP hierarchy are…
In this paper we study modular $G$-equivariant fusion categories and their extended Verlinde algebras. We dicuss settings in which fusion rules are diagonalizable. In particular, when $G = \mathbb{Z}_{2}$ we generalize the Verlinde formula.…
In this paper, we construct the super Witt algebra and super Virasoro algebra in the framework of the $\mathcal{R}(p,q)$-deformed quantum algebras. Moreover, we perform the super $\mathcal{R}(p,q)$-deformed Witt $n$-algebra, the…
The fusion rules in $\mathrm{Rep}_f D(G)$ for a finite group $G$ can be computed in terms of character inner products. Using an explicit formula for these fusion rules, we show that $\mathrm{Rep}_f D(G)$ is multiplicity free for two…
Prospects for SO(10) as a minimal grand unification group have recently been heightened by several considerations such as the MSW resolution of the solar neutrino puzzle, baryogenesis, possibility for understanding fermion masses etc. I…
The partition algebras are algebras of diagrams (which contain the group algebra of the symmetric group and the Brauer algebra) such that the multiplication is given by a combinatorial rule and such that the structure constants of the…
For any non-unitary model with central charge c(2,q) the path spaces associated to a certain fusion graph are isomorphic to the irreducible Virasoro highest weight modules.
A new quasi-particle basis of states is presented for all the irreducible modules of the M(3,p) models. It is formulated in terms of a combination of Virasoro modes and the modes of the field phi_{2,1}. This leads to a fermionic expression…
The SL(2,Z) representation $\pi$ on the center of the restricted quantum group U_{q}sl(2) at the primitive 2p-th root of unity is shown to be equivalent to the SL(2,Z) representation on the extended characters of the logarithmic (1,p)…