相关论文: Rogers-Ramanujan exact sequences and free represen…
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 use vertex operator algebras and intertwining operators to study certain substructures of standard $A_1^{(1)}$--modules, allowing us to conceptually obtain the classical Rogers--Ramanujan recursion. As a consequence we recover…
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…
Ramanujan recorded four reciprocity formulas for the Roger-Ramanujan continued fraction. Two reciprocity formulas each are also associated with the Ramanujan--G\"ollnitz--Gordon continued fraction and a level-13 analog of the…
We consider two different methods of associating vertex algebraic structures with the level $1$ principal subspaces for $U_q (\widehat{\mathfrak{sl}}_2)$. In the first approach, we introduce certain commutative operators and study the…
In this article we continue a previous work in which we have generalized the Rogers Ramanujan continued fraction (RR) introducing what we call, the Ramanujan-Quantities (RQ). We use the Mathematica package to give several modular equations…
J. Lepowsky and R. L. Wilson initiated the approach to combinatorial Rogers-Ramanujan type identities via the vertex operator constructions of representations of affine Lie algebras. In a joint work with Arne Meurman this approach is…
In this article we present evaluations of continued fractions studied by Ramanujan. More precisely we give the complete polynomial equations of Rogers-Ramanujan and other continued fractions, using tools from the elementary theory of the…
Hatayama et al. described generalized Rogers--Ramanujan (GRR) expressions for the string functions of the singlet representation of twisted affine algebras. We give here such GRR expressions for some non-singlet string functions. In the…
The characters of parafermionic conformal field theories are given by the string functions of affine algebras, which are either twisted or untwisted algebras. Expressions for these characters as generalized Rogers Ramanujan algebras have…
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…
The Rogers-Ramanujan-Gordon identities generalize the classical partition identities discovered independently by L. J. Rogers and S. Ramanujan. In 2021, Afsharijoo provided a commutative algebra proof of the Rogers-Ramanujan-Gordon…
Characters and linear combinations of characters that admit a fermionic sum representation as well as a factorized form are considered for some minimal Virasoro models. As a consequence, various Rogers-Ramanujan type identities are…
We study the structure and representations of a family of vertex algebras obtained from affine superalgebras by quantum reduction. As an application, we obtain in a unified way free field realizations and determinant formulas for all…
Arc spaces have been introduced in algebraic geometry as a tool to study singularities but they show strong connections with combinatorics as well. Exploiting these relations we obtain a new approach to the classical Rogers-Ramanujan…
The generalized Fibonacci sequences are sequences $\{f_n\}$ which satisfy the recurrence $f_n(s, t) = sf_{n - 1}(s, t) + tf_{n - 2}(s, t)$ ($s, t \in \mathbb{Z}$) with initial conditions $f_0(s, t) = 0$ and $f_1(s, t) = 1$. In a recent…
AGT correspondence and its generalizations attracted a great deal of attention recently. In particular it was suggested that $U(r)$ instantons on $R^4/Z_p$ describe the conformal blocks of the coset ${\cal A}(r,p)=U(1)\times sl(p)_r\times…
We study the classical and quantum $G$ extended superconformal algebras from the hamiltonian reduction of affine Lie superalgebras, with even subalgebras $G\oplus sl(2)$. At the classical level we obtain generic formulas for the Poisson…
J.~Lepowsky and R.~L.~Wilson initiated the approach to combinatorial Rogers-Ramanujan type identities via vertex operator constructions of standard (i.e. integrable highest weight) representations of affine Kac-Moody Lie algebras.…
The aim of this paper is to study the convergence and divergence of the Rogers-Ramanujan and the generalized Rogers-Ramanujan continued fractions on the unit circle. We provide an example of an uncountable set of measure zero on which the…