(k,r)-admissible configurations and intertwining operators

Quasi-particle fermionic formulas for $(k,3)$-admissible configurations

We construct new monomial quasi-particle bases of Feigin-Stoyanovsky's type subspaces for affine Lie algebra $\mathfrak{sl}(3,\mathbb{C})^{\widetilde{}}$ from which the known fermionic-type formulas for $(k,3)$-admissible configurations follow naturally. In the proof we use vertex operator algebra relations for standard modules and coefficients of intertwining operators.

Vertex Operators of Admissible Modules of $U_q(C^{(1)}_n)$

Using our recent bosonic realization of $U_q(\widehat{sp}_{2n})$, we construct explicitly the vertex operators for the level -1/2 modules of $U_q(\widehat{sp}_{2n})$ using bosonic fields. Our method contains a detailed analysis of all the q-intertwining relations.

Fermionic formulas for (k, 3)-admissible configurations

We obtain the fermionic formulas for the characters of (k, r)-admissible configurations in the case of r=2 and r=3. This combinatorial object appears as a label of a basis of certain subspace $W(Λ)$ of level-$k$ integrable highest weight module of $\hat{sl}_{r}$. The dual space of $W(Λ)$ is embedded into the space of symmetric polynomials. We introduce a filtration on this space and determine the components of the associated graded space explicitly by using vertex operators. This implies a fermionic formula for the character of $W(Λ)$.

扭曲结合代数与交织算子

Twisted associative algebras and intertwining operators

研究具有特定自同构的顶点代数，通过构造结合代数，建立了不同类型\(V\)模范畴间的同构及等价关系，还针对三个可交换自同构构造双模，证明了特定交织算子空间的同构。

简单可允许仿射$\mathfrak{sl}(2)$和$\mathcal{N}=2$超共形顶点算子超代数上权模的融合规则与刚性

Fusion rules and rigidity for weight modules over the simple admissible affine $\mathfrak{sl}(2)$ and $\mathcal{N}=2$ superconformal vertex operator superalgebras

研究简单$\mathfrak{sl}(2)$和$\mathcal{N}=2$超共形顶点算子代数上权模，证明其权模范畴刚性及融合积分解公式成立，通过积分屏蔽流开发新技术，给出$\mathfrak{sl}(2)$对数交织算子显式公式。

A proof of the fusion rules theorem

We prove that the space of intertwining operators associated with certain admissible modules over vertex operator algebras is isomorphic to a quotient of the vector space of conformal blocks on a three-pointed rational curve defined by the same data. This provides a new proof and alternative version of Frenkel and Zhu's fusion rules theorem in terms of the dimension of certain bimodules over Zhu's algebra, without the assumption of rationality.