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Cuipo Jiang

Publications and source records attributed to Cuipo Jiang.

At least 37 records · Page 2Linked to original sources
arXiv2019

Fusion rules for $\mathbb{Z}_{2}$-orbifolds of affine and parafermion vertex operator algebras

This paper is about the orbifold theory of affine and parafermion vertex operator algebras. It is known that the parafermion vertex operator algebra $K(sl_2,k)$ associated to the integrable highest weight modules for the affine Kac-Moody algebra $A_1^{(1)}$ is the building block of the general parafermion vertex operator $K(\mathfrak{g},k)$ for any finite dimensional simple Lie algebra $\mathfrak{g}$ and any positive integer $k$. We first classify the irreducible modules of $\mathbb{Z}_{2}$-orbifold of the simple affine vertex operator algebra of type $A_1^{(1)}$ and determine their fusion rules. Then we study the representations of the $\mathbb{Z}_{2}$-orbifold of the parafermion vertex operator algebra $K(sl_2,k)$, we give the quantum dimensions, and more technically, fusion rules for the $\mathbb{Z}_{2}$-orbifold of the parafermion vertex operator algebra $K(sl_2,k)$ are completely determined.

math.QA↗
arXiv2017

Coset Vertex Operator Algebras and $\W$-Algebras

We give an explicit description for the weight three generator of the coset vertex operator algebra $C_{L_{\widehat{\sl_{n}}}(l,0)\otimes L_{\widehat{\sl_{n}}}(1,0)}(L_{\widehat{\sl_{n}}}(l+1,0))$, for $n\geq 2, l\geq 1$. Furthermore, we prove that the commutant $C_{L_{\widehat{\sl_{3}}}(l,0)\otimes L_{\widehat{\sl_{3}}}(1,0)}(L_{\widehat{\sl_{3}}}(l+1,0))$ is isomorphic to the $\W$-algebra $\W_{-3+\frac{l+3}{l+4}}(\sl_3)$, which confirms the conjecture for the $\sl_3$ case that $C_{L_{\widehat{\frak g}}(l,0)\otimes L_{\widehat{\frak g}}(1,0)}(L_{\widehat{\frak g}}(l+1,0))$ is isomorphic to $\W_{-h+\frac{l+h}{l+h+1}}(\frak g)$ for simply-laced Lie algebras ${\frak g}$ with its Coxeter number $h$ for a positive integer $l$.

math.RT↗
arXiv2013

On a category of $gl_{\infty}$-modules

We study a particular category ${\cal{C}}$ of $\gl_{\infty}$-modules and a subcategory ${\cal{C}}_{int}$ of integrable $\gl_{\infty}$-modules. As the main results, we classify the irreducible modules in these two categories and we show that every module in category ${\cal{C}}_{int}$ is semi-simple. Furthermore, we determine the decomposition of the tensor products of irreducible modules in category ${\cal{C}}_{int}$.

math.QA↗
arXiv2013

Associating quantum vertex algebras to Lie algebra $\gl_{\infty}$

In this paper, we present a canonical association of quantum vertex algebras and their $ϕ$-coordinated modules to Lie algebra $\gl_{\infty}$ and its 1-dimensional central extension. To this end we construct and make use of another closely related infinite-dimensional Lie algebra.

math.QA↗
arXiv2012

Representations of the vertex operator algebra V_{L_{2}}^{A_{4}}

The rationality and C_2-cofiniteness of the orbifold vertex operator algebra V_{L_{2}}^{A_{4}} are established and all the irreducible modules are constructed and classified. This is part of classification of rational vertex operator algebras with c=1.

math.QA↗
arXiv2011

A characterization of the rational vertex operator algebra $V_{\Zα}^{+}$}: II

A characterization of vertex operator algebra $V_L^+$ for any rank one positive definite even lattice $L$ is given in terms of dimensions of homogeneous subspaces of small weights. This result reduces the classification of rational vertex operator algebras of central charge 1 to the characterization of three vertex operator algebras in the $E$-series of central charge one.

math.QA↗
arXiv2011

A characterization of vertex operator algebras $V_{Zα}^{+}$: I

A characterization of vertex operator algebra V_{Zα}^+ with (α,α)/2 not being a perfect square is given in terms of dimensions of homogeneous subspaces of small weights. This result contributes to the classification of rational vertex operator algebras of central charge 1.

math.QA↗
arXiv2011

Extension of vertex operator algebra $V_{\hat{H}_{4}}(\ell,0)$

We classify the irreducible restricted modules for the affine Nappi-Witten Lie algebra $\hat{H}_{4}$ with some natural conditions. It turns out the representation theory of $\hat{H}_{4}$ is quite different from the theory of representations of Heisenberg algebras. We also study the extension of the vertex operator algebra $V_{\hat{H}_{4}}(\ell,0)$ by the even lattice $L$. We give the structure of the extension $V_{\hat{H}_{4}}(\ell,0)\otimes \C[L]$ and its irreducible modules via irreducible representations of $V_{\hat{H}_{4}}(\ell,0)$ viewed as a vertex algebra.

math.QA↗
arXiv2011

Representations of affine Nappi-Witten algebras

In this paper, we study the representation theory for the affine Lie algebra $\H$ associated to the Nappi-Witten model $H_{4}$. We classify all the irreducible highest weight modules of $\H$. Furthermore, we give a necessary and sufficient condition for each $\H$-(generalized) Verma module to be irreducible. For reducible ones, we characterize all the linearly independent singular vectors. Finally, we construct Wakimoto type modules for these Lie algebras and interpret this construction in terms of vertex operator algebras and their modules.

math.QA↗
arXiv2008

Structure of the extended Schrodinger-Virasoro Lie algebra

In this paper, we study the derivations, the central extensions and the automorphism group of the extended Schrodinger-Virasoro Lie algebra, introduced by J. Unterberger in the context of two-dimensional conformal field theory and statistical physics. Moreover, we show that the extended Schrodinger-Virasoro Lie algebra is an infinite-dimensional complete Lie algebra and the universal central extension of the extended Schrodinger-Virasoro Lie algebra in the category of Leibniz algebras is the same as that in the category of Lie algebras.

math.RA↗
arXiv2007

Representations for the non-graded Virasoro-like algebra

It is proved that an irreducible module over the non-graded Virasoro-like algebra, which satisfies a natural condition, is a GHW module or uniformly bounded. Furthermore, the classification of some uniformly bounded modules is given.

math.RT↗