Related papers: Modular forms associated with the Monster module
Andrews recently introduced k-marked Durfee symbols, which are a generalization of partitions that are connected to moments of Dyson's rank statistic. He used these connections to find identities relating their generating functions as well…
The purpose of this note is to define and construct highest weight modules for Felder's elliptic quantum groups. This is done by using exchange matrices for intertwining operators between (not necessarily finite-dimensional) modules over…
False theta functions are functions that are closely related to classical theta functions and mock theta functions. In this paper, we study their modular properties at all ranks by forming modular completions analogous to modular…
We investigate the representations of a class of conformal Galilei algebras in one spatial dimension with central extension. This is done by explicitly constructing all singular vectors within the Verma modules, proving their completeness…
We show that the generating series of traces of reciprocal singular moduli is a mixed mock modular form of weight $3/2$ whose shadow is given by a linear combination of products of unary and binary theta functions. To prove these results,…
We express recent double-sums studied by Wang, Yee, and Liu in terms of two types of Hecke-type double-sum building blocks. When possible we determine the (mock) modularity. We also express a recent $q$-hypergeometric function of Andrews as…
We give bounds on the degree of generators for the ideal of relations of the graded algebras of modular forms with coefficients in $\mathbb{Q}$ over congruence subgroups $\Gamma_0(N)$ for $N$ satisfying some congruence conditions and for…
We show the vertex operator formalism for the quiver gauge theory partition function and the $qq$-character of highest-weight module on quiver, both associated with the integral over the quiver variety.
We investigate correspondence functors, namely the functors from the category of finite sets and correspondences to the category of $k$-modules, where $k$ is a commutative ring.They have various specific properties which do not hold for…
Vector-like quarks (VLQs) are attractive extensions to the Standard Model. They mix with the SM quarks and can lead to rich phenomenology. Determination of VLQ's interaction structure with the SM is then an important issue, which can be…
We revisit the classical Goddard-Kent-Olive coset construction. We find the formulas for the highest weight vectors in coset decomposition and calculate their norms. We also derive formulas for matrix elements of natural vertex operators…
The main focus of the present paper is to investigate several generating functions for a certain classes of functions associated to the Fox-Wright functions. In particular, certain generating functions for a class of function involving the…
We give a new method for constructing vector-valued modular forms from singular scalar-valued ones. As an application we prove the identity between two remarkable spaces of vector-valued modular forms which seem to be unrelated at a first…
We derive generating functions for the ranks of pre-modular categories associated to quantum groups at roots of unity.
Let G=GL_n be the general linear group over an algebraically closed field k and let g=gl_n be its Lie algebra. Let U be the subgroup of G which consists of the upper unitriangular matrices. Let k[g] be the algebra of regular functions on…
It has been shown that the longitudinal mode of a massive vector boson can be produced by inflationary fluctuations and account for the dark matter content of the Universe. In this work we examine the possibility of instead producing the…
We present a dimension formula for spaces of vector-valued modular forms of integer weight in case the associated multiplier system has finite image, and discuss the weight distribution of the module generators of holomorphic and cusp…
In this article, we will show that the category of biset functors can be regarded as a reflective monoidal subcategory of the category of Mackey functors on the 2-category of finite groupoids. This reflective subcategory is equivalent to…
Mock modular forms have their origins in Ramanujan's pioneering work on mock theta functions. In a 1975 paper, Zagier proved certain transformation properties of the generating function of the Hurwitz class numbers $H(n)$ for the…
We exhibit an infinite family of vector-valued mock theta functions indexed by positive integers coprime to $6$. These are built from specializations of Dyson's rank generating function and related functions studied by Watson, Gordon, and…