相关论文: Presentations of the principal subspaces of the hi…
Using completions of certain universal enveloping algebras, we provide a natural setting for families of defining relations for the principal subspaces of standard modules for untwisted affine Lie algebras. We also use the theory of vertex…
We use the theory of vertex operator algebras and intertwining operators to obtain systems of q-difference equations satisfied by the graded dimensions of the principal subspaces of certain level k standard modules for \hat{\goth{sl}(3)}.…
We study the principal subspaces of higher level standard $A_2^{(2)}$-modules, extending earlier work in the level one case, by Calinescu, Lepowsky, and Milas. We prove natural presentations of principal subspaces and also of certain…
We study the principal subspaces, introduced by B. Feigin and A. Stoyanovsky, of the level 1 standard modules for $\hat{\goth{sl}(l+1)}$ with $l \geq 2$. In this paper we construct exact sequences which give us a complete set of recursions…
We give an a priori proof of the known presentations of (that is, completeness of families of relations for) the principal subspaces of all the standard A_1^(1)-modules. These presentations had been used by Capparelli, Lepowsky and Milas…
Using the theory of intertwining operators for vertex operator algebras we show that the graded dimensions of the principal subspaces associated to the standard modules for $\hat{\goth{sl}(2)}$ satisfy certain classical recursion formulas…
This is the third in a series of papers studying the vertex-algebraic structure of principal subspaces of twisted modules for lattice vertex operator algebras. We focus primarily on lattices $L$ whose Gram matrix contains only non-negative…
This is the first in a series of papers in which we study vertex-algebraic structure of Feigin-Stoyanovsky's principal subspaces associated to standard modules for both untwisted and twisted affine Lie algebras. A key idea is to prove…
Standard subspaces are closed real subspaces of a complex Hilbert space that appear naturally in Tomita-Takesaki modular theory and its applications to quantum field theory. In this article, inclusions of standard subspaces are studied…
We construct vertex algebraic intertwining operators among certain generalized Verma modules for $\widehat{\mathfrak{sl}(2,\mathbb{C})}$ and calculate the corresponding fusion rules. Additionally, we show that under some conditions these…
Generalizing some of our earlier work, we prove natural presentations of the principal subspaces of the level one standard modules for the untwisted affine Lie algebras of types A, D and E, and also of certain related spaces. As a…
Extending earlier work of the authors, this is the first in a series of papers devoted to the vertex-algebraic structure of principal subspaces of standard modules for twisted affine Kac-Moody algebras. In this part, we develop the…
In the classical operator theory, there are several versions of spectra, related to special classes of operators (Fredholm, semi-Fredholm, upper/lower semi-Fredholm,etc.). We generalize these notions for adjointable operators on Hilbert…
By using the known description of combinatorial bases for Feigin-Stoyanovsky's type subspaces of standard modules for affine Lie algebra $\mathfrak{sl}(l+1,\mathbb{C})^{\widetilde{}}$, as well as certain intertwining operators between…
Let $\text{GL}(n) = \text{GL}(n, {\mathbb C})$ denote the complex general linear group and let $G \subset \text{GL}(n)$ be one of the classical complex subgroups $\text{O}(n)$, $\text{SO}(n)$, and $\text{Sp}(2k)$ (in the case $n = 2k$). We…
Let $V$ be a vertex operator algebra and $A^{\infty}(V)$ and $A^{N}(V)$ for $N\in \mathbb{N}$ the associative algebras introduced by the author in [H5]. For a lower-bounded generalized $V$-module $W$, we give $W$ a structure of graded…
A notion of intermediate vertex subalgebras of lattice vertex operator algebras is introduced, as a generalization of the notion of principal subspaces. Bases and the graded dimensions of such subalgebras are given.As an application, it is…
We notice that for any positive integer $k$, the set of $(1,2)$-specialized characters of level $k$ standard $A_{1}^{(1)}$-modules is the same as the set of rescaled graded dimensions of the subspaces of level $2k+1$ standard…
We construct the nonlinear $W(sl(N+3),sl(3))$ algebras and find the spectrum of values of the central charge that gives rise, by contracting the $W(sl(N+3),sl(3))$ algebras, to a $W_3$ algebra belonging to the coset…
Exact sequences of Feigin-Stoyanovsky's type subspaces for affine Lie algebra $\mathfrak{sl}(l+1,\mathbb{C})^{\widetilde{}}$ lead to systems of recurrence relations for formal characters of those subspaces. By solving the corresponding…