Related papers: Level Two String Functions and Rogers Ramanujan Ty…
We present systems of parabosons and parafermions in the context of Lie algebras, Lie superalgebras, $\mathbf{{\mathbb Z}_2\ \times {\mathbb Z}_2}$-graded Lie algebras and $\mathbf{{\mathbb Z}_2\ \times {\mathbb Z}_2}$-graded Lie…
We introduce two q-analogues of the 2D-Hermite polynomials which are functions of two complex variables. We derive explicit formulas, orthogonality relations, raising and lowering operator relations, generating functions, and Rodrigues…
We study higher level Regge resonances of open superstrings, focusing on the universal part of the Neveu-Schwarz sector common to all D-brane realizations of the standard model. For Regge states with masses far above the fundamental string…
Recently, $4$-regular partitions into distinct parts are connected with a family of overpartitions. In this paper, we provide a uniform extension of two relations due to Andrews for the two types of partitions. Such an extension is made…
Fix $n \geq 2$ an integer, and let $F$ be a totally real number field. We derive estimates for the finite parts of the $L$-functions of irreducible cuspidal $\operatorname{GL}_n({\bf{A}}_F)$-automorphic representations twisted by class…
Recently Conrey, Farmer and Zirnbauer conjectured formulas for the averages over a family of ratios of products of shifted L-functions. Their L-functions Ratios Conjecture predicts both the main and lower order terms for many problems,…
Graded contractions of certain non-toral $\mathbb{Z}_2^3$-gradings on the simple Lie algebras $\mathfrak{so}(7,\mathbb C)$ and $\f{so}(8,\mathbb C)$ are classified up to two notions of equivalence. In particular, there arise two large…
Several classes of DNR functions are characterized in terms of Kolmogorov complexity. In particular, a set of natural numbers A can wtt-compute a DNR function iff there is a nontrivial recursive lower bound on the Kolmogorov complexity of…
This is the second paper of a series of papers on a version of categories $\mathcal{O}$ for root-reductive Lie algebras. Let $\mathfrak{g}$ be a root-reductive Lie algebra over an algebraically closed field $\mathbb{K}$ of characteristic…
The corrections to the tree-level effective action for the bosonic string up to second order in $\alpha'$ are fixed by requiring its dimensional reduction to $26-d$ dimensions to be compatible with $O(d,d)$ symmetry. The result is in…
A careful treatment of closed string BRST cohomology shows that there are more discrete states and associated symmetries in $D=2$ string theory than has been recognized hitherto. The full structure, at the $SU(2)$ radius, has a natural…
We investigate feasible computation over a fairly general notion of data and codata. Specifically, we present a direct Bellantoni-Cook-style normal/safe typed programming formalism, RS1, that expresses feasible structural recursions and…
We complete the program for determining the full automorphism groups of all parafermion vertex operator algebras associated with simple Lie algebras and positive integral levels. We show that the full automorphism group of the parafermion…
The ground field in the text is of characteristic 2. The classification of modulo 2 gradings of simple Lie algebras is vital for the classification of simple finite-dimensional Lie superalgebras: with each grading, a simple Lie superalgebra…
Inspired by a number of recent papers by Corteel, Dousse, Foda, Uncu and Welsh on cylindric partitions and Rogers-Ramanujan-type identities, we obtain the $\mathrm{A}_2$ (or $\mathrm{A}_2^{(1)}$) analogues of the celebrated Andrews-Gordon…
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…
Kanade and Russell conjectured several Rogers-Ramanujan-type partition identities, some of which are related to level $2$ characters of the affine Lie algebra $A_9^{(2)}$. Many of these conjectures have been proved by Bringmann,…
We discuss the homological aspects of the connection between quantum string generating function and the formal power series associated to the dimensions of chains and homologies of suitable Lie algebras. Our analysis can be considered as a…
We define the partition and $n$-point functions for a vertex operator algebra on a genus two Riemann surface formed by sewing two tori together. We obtain closed formulas for the genus two partition function for the Heisenberg free bosonic…
In this paper, we combined two types of partitions and introduced 2-colored Rogers-Ramanujan partitions. By finding some functional equations and using a constructive method, some identities have been found. Some Overpartition identities…