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Honglian Zhang

Publications and source records attributed to Honglian Zhang.

29 records · Page 2Linked to original sources
arXiv2018

Poincaré series, exponents of affine Lie algebras, and McKay-Slodowy correspondence

Let $N$ be a normal subgroup of a finite group $G$ and $V$ be a fixed finite-dimensional $G$-module. The Poincaré series for the multiplicities of induced modules and restriction modules in the tensor algebra $T(V)=\oplus_{k \geq 0}V^{\otimes k}$ are studied in connection with the McKay-Slodowy correspondence. In particular, it is shown that the closed formulas for the Poincaré series associated with the distinguished pairs of subgroups of $\mathrm{SU}_2$ give rise to the exponents of all untwisted and twisted affine Lie algebras except ${\rm A}_{2n}^{(1)}$.

math.QA↗
arXiv2018

A class of non-weight modules over the Schrödinger-Virasoro algebras

We construct and classify the free $U(\mathbb{C}L_0\oplus \mathbb{C}M_0\oplus\mathbb{C}Y_0)$-modules of rank $1$ over the Schrödinger-Virasoro algebra $\mathfrak{sv}(s)$ for $s=0$.Moreover, we show that the class of free $U(\mathbb{C}L_0\oplus\mathbb{C}M_0)$-modules of rank $1$ over the Schrödinger-Virasoro algebra $\mathfrak{sv}(s)$ for $s=\frac{1}{2}$ is nonexistent.

math.RT↗
arXiv2016

Two-parameter twisted quantum affine algebras

We establish Drinfeld realization for the two-parameter twisted quantum affine algebras using a new method. The Hopf algebra structure for Drinfeld generators is given for both untwisted and twisted two-parameter quantum affine algebras, which include the quantum affine algebras as special cases.

math.QA↗
arXiv2016

Drinfeld realization of quantum twisted affine algebras via braid group

The Drinfled realization of quantum affine algebras has been tremendously useful since its discovery. Combining techniques of Beck and Nakajima with our previous approach, we give a complete and conceptual proof of the Drinfeld realization for the twisted quantum affine algebras using Lusztig's twisted braid group action.

math.QA↗
arXiv2015

Fermionic realization of two-parameter quantum affine algebra $U_{r,s}(C_l^{(1)})$

We construct a Fock space representation and the action of the two-parameter quantum algebra $U_{r,s}(\frak{gl}_{\infty})$ using extended Young diagrams. In particular, we obtain an integrable representation of the two-parameter quantum affine algebra of type $C_n^{(1)}$ which is a two-parameter generalization of Kang-Misra-Miwa's realization.

math.QA↗
arXiv2014

Generating Functions with $τ$-Invariance and Vertex Representations of Quantum Affine Algebras $U_{r,s}(\widehat{\mathfrak{g}})$ (I): Simply-laced Cases

We put forward the exact version of two-parameter generating functions with $τ$-invariance, which allows us to give a unified and inherent definition for the Drinfeld realization of two-parameter quantum affine algebras for all the untwisted types. As verification, we first construct their level-one vertex representations of $U_{r,s}(\widehat{\mathfrak{g}})$ for simply-laced types, which in turn well-detect the effectiveness of our definitions both for $(r,s)$-generating functions and $(r,s)$-Drinfeld realization in the framework of establishing the two-parameter vertex representation theory.

math.QA↗
arXiv2008

Two-parameter Quantum Affine Algebra $U_{r,s}(\widehat{\frak {sl}_n})$, Drinfel'd Realization and Quantum Affine Lyndon Basis

We further define two-parameter quantum affine algebra $U_{r,s}(\widehat{\frak {sl}_n})$ $(n>2)$ after the work on the finite cases (see [BW1], [BGH1], [HS] & [BH]), which turns out to be a Drinfel'd double. Of importance for the quantum {\it affine} cases is that we can work out the compatible two-parameter version of the Drinfel'd realization as a quantum affinization of $U_{r,s}(\frak{sl}_n)$ and establish the Drinfel'd isomorphism Theorem in the two-parameter setting, via developing a new combinatorial approach (quantum calculation) to the quantum {\it affine} Lyndon basis we present (with an explicit valid algorithm based on the use of Drinfel'd generators).

math.QA↗