Related papers: Gamma factors of level zero supercuspidal represen…

Supersymmetry transformations may be represented by unitary operators in a formulation of supersymmetry without numbers that anti-commute. The physical relevance of this formulation hinges on whether or not one may add states of even and…

The description of irreducible finite dimensional representations of finite dimensional solvable Lie superalgebras over complex numbers given by V.~Kac is refined. In reality these representations are not just induced from a polarization…

We provide upper and lower bounds on the semileptonic weak decay form factors for $B \to D^(*)$ and $\Lambda_b \to \Lambda_c$ decays by utilizing inclusive heavy quark effective theory sum rules. These bounds are calculated to second order…

Geometric representations provide a principled framework for structuring the description of latent constructs and clarifying sources of uncertainty in their dimensional characterisation. We introduce a novel geometric representation of…

We exhibit a basis for the space of spherical characters of a distinguished supercuspidal representation $\pi$ of a connected reductive $p$-adic group, subject to the assumption that $\pi$ is obtained via induction from a representation of…

The minimal irreducible representations of $U_q[gl(m|n)]$, i.e. those irreducible representations that are also irreducible under $U_q[osp(m|n)]$ are investigated and shown to be affinizable to give irreducible representations of the…

Let $(\pi,V)$ be a $GL_n(\mathbb{R})$-distinguished, irreducible, admissible representation of $GL_n(\mathbb{C})$, let $\pi'$ be an irreducible, admissible, $GL_m(\mathbb{R})$-distinguished representation of $GL_m(\mathbb{C})$, and let…

We define the twisted doubling zeta integrals of Cai-Friedberg-Ginzburg-Kaplan in the setting of algebraic families. We then prove a rationality result and a functional equation for these zeta integrals. This allows us to define an…

Irreducible representations (irreps) of $\mathbb{Z}_2^2$-graded supersymmetry algebra of ${\cal N}=2$ are obtained by the method of induced representation and they are used to derive $\mathbb{Z}_2^2$-graded supersymmetric classical actions.…

Let $k$ be a finite field of characteristic $p$. In the 1960s, Kondo attached non-abelian Gauss sums to irreducible $\mathbb{C}$-representations of $\mathrm{GL}_n(k)$, and computed them in terms of Green parameters. On the other hand, the…

In this paper, we parametrize certain irreducible supercuspidal representations of U(1,1) and U(2) via explicit induction data. The parametrization depends on traceless elements of negative valuation in a quadratic extension of base field.…

We study an exponential sum over Laplacian eigenvalues $\lambda_{j} = 1/4+t_{j}^{2}$ with $t_{j} \leqslant T$ for Maass cusp forms on $\Gamma \backslash \mathbb{H}$, where $\Gamma$ is a cofinite Fuchsian group acting on the upper half-plane…

Let $G$ be the group of rational points of a general linear group over a non-archimedean local field $F$. We show that certain representations of open, compact-mod-centre subgroups of $G$, (the maximal simple types of Bushnell and Kutzko)…

We use Kuperberg's diagrammatic description of the space of homomorphisms between fundamental representations of $G_2$ to give explicit recursive formulas for the idempotent projecting to the highest weight irreducible summand in each…

Upper and lower bounds are established on the Lambda_b -> Lambda_c semileptonic decay form factors by utilizing inclusive heavy-quark-effective-theory sum rules. These bounds are calculated to leading order in Lambda_QCD/m_Q and alpha_s.…

This paper proposes a reformulation of the Riemann Xi function in order to investigate its properties. The reformulated function, which depicts the Xi function as the weighted sum of incomplete gamma functions, is validated, and a number of…

We define an absolutely convergent series for the upper incomplete Gamma function $\Gamma(s,z)$ for $z\geq 1$ and $s\in \mathbb{C}$. We express this series using certain polynomials which we define using the Stirling numbers of the first…

We give the decomposition into irreducible factors of Weil representations of the symplectic groups at even levels, generalizing previous decompositions at odd levels. We then derive the decomposition of the quantum representations of…

We introduce a local zeta-function for an irreducible admissible supercuspidal representation $\pi$ of the metaplectic double cover of $\SL_2$ over a non-archimedean local field of characteristic zero. We prove a functional equation of the…

We display the construction of a twisted superalgebra for the N=1 Euclidian supergravity on 4-manifolds with an almost complex structure. It acts on a representation of twisted supersymmetry made of forms with odd and even statistics and it…