arXiv subjects
Publications and source records attributed to Shaobin Tan.
In this paper, the conjugate-linear anti-involutions and the unitary irreducible modules of the intermediate series over the twisted Heisenberg-Virasoro algebra are classified respectively. We prove that any unitary irreducible module of the intermediate series over the twisted Heisenberg-Virasoro algebra is of the form $\mathcal{A}_{a,b,c}$ for $a\in \mathbb{R}, b\in 1/2+\sqrt{-1}\mathbb{R}, c\in \mathbb{C}.$
In this paper, conjugate-linear anti-involutions and unitary Harish-Chandra modules over the Schrödinger-Virasoro algebra are studied. It is proved that there are only two classes conjugate-linear anti-involutions over the Schrödinger-Virasoro algebra. The main result of this paper is that a unitary Harish-Chandra module over the Schrödinger-Virasoro algebra is simply a unitary Harish-Chandra module over the Virasoro algebra.
Let $G$ be a real quaternionic classical group $\GL_n(\bH)$, $\Sp(p,q)$ or $\oO^*(2n)$. We define an extension $\breve G$ of $G$ with the following property: it contains $G$ as a subgroup of index two, and for every $x\in G$, there is an element $\breve g\in \breve G\setminus G$ such that $\breve g x\breve{g}^{-1}=x^{-1}$. This is similar to Moeglin-Vigneras-Waldspurger's extensions of non-quaternionic classical groups.
In this paper, Whittaker modules for the Schrödinger-Virasoro algebra $\mathfrak{sv}$ are defined. The Whittaker vectors and the irreducibility of the Whittaker modules are studied. $\mathfrak{sv}$ has a triangular decomposition according to the Cartan algebra $\mathfrak{h}:$ $$\mathfrak{sv}=\mathfrak{sv}^{-}\oplus\mathfrak{h}\oplus\mathfrak{sv}^{+}.$$ For any Lie algebra homomorphism $ψ:\mathfrak{sv}^{+}\to\mathbb{C}$, we can define Whittaker modules of type $ψ.$ When $ψ$ is nonsingular, the Whittaker vectors, the irreducibility and the classification of Whittaker modules are completely determined. When $ψ$ is singular, by constructing some special Whittaker vectors, we find that the Whittaker modules are all reducible. Moreover, we get some more precise results for special $ψ$.
We study twisted modules for (weak) quantum vertex algebras and we give a conceptual construction of (weak) quantum vertex algebras and their twisted modules. As an application we construct and classify irreducible twisted modules for a certain family of quantum vertex algebras.
Let $\mathbb{F}$ be a field of characteristic 0, $G$ an additive subgroup of $\mathbb{F}$, $α\in \mathbb{F}$ satisfying $α\notin G, 2α\in G$. We define a class of infinite-dimensional Lie algebras which are called generalized Schrödinger-Virasoro algebras and use $\mathfrak{gsv}[G,α]$ to denote the one corresponding to $G$ and $α$. In this paper the automorphism group and irreducibility of Verma modules for $\mathfrak{gsv}[G,α]$ are completely determined.
In this paper we study the representation theory for certain ``half lattice vertex algebras.'' In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these vertex algebras are related to the representation theory of some associative algebras.
We present a general vertex operator construction based on the Fock space for an affine Lie algebras of type $A$. This construction allows us to give a unified treatment for both the homogeneous and principle realizations of the affine Lie algebras $\hat{gl}_N$ as well as for some extended affine Lie algebras coordinatized by certain quantum tori.