7 problems

The paper considers the affine Lie algebra $\hat{\mathfrak g}$, its central element $\mathbf k$, and truncated vertex operator algebras $\hat{\mathbf F}_{k+h^\vee}$ and…

The Verlinde algebra isomorphism conjecture. For every homogeneous degree $z^n$ with $n\neq 0$, the map

Let $k$ be an even positive integer, and let $\mathfrak{g}$ be a twisted affine Lie algebra not of type $A_{2\ell}^{(2)}$. Let $P_k^+$ be the set of dominant weights at level $k$,…

Let $\mathfrak{g}$ be an affine Lie algebra of type $A_{2\ell}^{(2)}$, and fix an even level $2n$ with $n\in\mathbb{Z}_{>0}$. Let $P_{2n}$ denote the weights at level $2n$, let…

Non-negativity conjecture. These expansion coefficients are always polynomials with non-negative coefficients. The statement is presented as an observation based on sample computat…

Geometric realization conjecture. There is an increasing function $N:\mathbb{N}\to\mathbb{N}$ and a collection of isomorphisms

The $(1,p)$ models are logarithmic conformal field theories whose Verlinde algebra is nonsemisimple; denote this algebra by the Verlinde algebra of the $(1,p)$ model, and let a DAH…