Related papers: Borcherds Products on Unitary Group $U(2,1)$

Let $\{\lambda_f(n)\}_{n \geq 1}$ be the normalized Hecke eigenvalues of a given holomorphic cusp form $f$ of even weight $k$. We show under the assumption of the existence of Littlewood's type zero free region for $L(s, f, \chi)$, where…

In this article, we are interested in modular forms with non-vanishing central critical values and linear independence of Fourier coefficients of modular forms. The main ingredient is a generalization of a theorem due to VanderKam to…

In this note, we generalize the isomorphisms to the case when the discriminant form is not necessarily induced from real quadratic fields. In particular, this general setting includes all the subspaces with epsilon-conditions, only two…

We prove a converse theorem for the multiplicative Borcherds lift for lattices of square-free level whose associated discriminant group is anisotropic. This can be seen as generalization of Bruinier's results in \cite{Br2}, which provides a…

We give a combinatorial description (including explicit differential-form bases) for the cohomology groups of the space of n distinct nonzero complex numbers, with coefficients in rank-one local systems which are of finite monodromy around…

Explicit expressions are given for the actions and radial matrix elements of basic radial observables on multi-dimensional spaces in a continuous sequence of orthonormal bases for unitary SU(1,1) irreps. Explicit expressions are also given…

We construct the irreducible unipotent modules of the finite general linear groups using tableaux. Our construction is analogous to that of James (1976) for the symmetric groups, answering an open question as to whether such a construction…

Let $U_{q}^{-}(\mathfrak g)$ be the negative half of a quantum Borcherds-Bozec algebra $U_{q}(\mathfrak g)$ and $V(\lambda)$ be the irreducible highest weight module with $\lambda \in P^{+}$. In this paper, we investigate the structures,…

Unextendible product bases (UPBs) play a key role in the study of quantum entanglement and nonlocality. A famous open question is whether there exist genuinely unextendible product bases (GUPBs), namely multipartite product bases that are…

A modular grid is a pair of sequences $(f_m)_m$ and $(g_n)_n$ of weakly holomorphic modular forms such that for almost all $m$ and $n$, the coefficient of $q^n$ in $f_m$ is the negative of the coefficient of $q^m$ in $g_n$. Zagier proved…

In this work, Ramanujan type congruences modulo powers of primes $p \ge 5$ are derived for a general class of products that are modular forms of level $p$. These products are constructed in terms of Klein forms and subsume generating…

Let $V(\lambda)$ be the irreducible lowest weight $U_q(D(N,1))$-module with lowest weight $\lambda$. Assume $\lambda = n_0\omega_0-\sum_{i=0}^{N}n_i\omega_i$, where $\omega_0$ is the fundamental weight corresponding to the unique odd coroot…

We study the property of being strongly weakly compactly generated (and some relatives) in projective tensor products of Banach spaces. Our main result is as follows. Let $1<p,q<\infty$ be such that $1/p+1/q\geq 1$. Let $X$ (resp., $Y$) be…

We construct invariant complex product (hyperparacomplex, indefinite quaternion) structures on the manifolds underlying the real noncompact simple Lie groups $SL(2m-1,\RR)$, $SU(m,m-1)$ and $SL(2m-1,\CC)^\RR$. We show that on the last two…

We study the coefficients of a natural basis for the space of weak harmonic Maass forms of weight $5/2$ on the full modular group. The non-holomorphic part of the first element of this infinite basis encodes the values of the partition…

We count the connected components in the moduli space of PU(p,q)-representations of the fundamental group for a closed oriented surface. The components are labelled by pairs of integers which arise as topological invariants of the flat…

Let k be a field, q in k. We derive a cup product formula on the Hochschild cohomology ring of a family Lambda_q of quiver algebras. Using this formula, we determine a subalgebra of k[x,y] isomorphic to Hochschild cohomology modulo N, where…

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…

We use Poincar\'e series of $ K $-finite matrix coefficients of genuine integrable representations of the metaplectic cover of $ \mathrm{SL}_2(\mathbb R) $ to construct a spanning set for the space of cusp forms $ S_m(\Gamma,\chi) $, where…

We relate the canonical basis of the Fock space representation of the quantum affine algebra $U_q(\widehat{\mathfrak{gl}}_{n})$, as defined by Leclerc and Thibon, to the canonical basis of its restriction to $U_q(\mathfrak{sl}_{n})$,…