Related papers: A new proof of Harish-Chandra's integral formula

We consider a dual pair $(G, G')$, in the sense of Howe, with G compact acting on $L^2(\mathbb{R}^n)$, for an appropriate $n$, via the Weil representation $\omega$. Let $\tilde{\mathrm{G}}$ be the preimage of G in the metaplectic group.…

For a (Reimannian) symmetric space $G/K$ of compact type, the natural action of $G$ on its complexification $G^{\mathbb C}/K^{\mathbb C}$ (which is an anti-Kaehler symmetric space) is one of the isometric actions called ``Hermann type…

Li-Zinger's hyperplane theorem states that the genus one GW-invariants of the quintic threefold is the sum of its reduced genus one GW-invariants and 1/12 multiplies of its genus zero GW-invariants. We apply the Guffin-Sharpe-Witten's…

In this paper, we classify all simple Harish-Chandra modules over the super affine-Virasoro algebra $\widehat{\mathcal{L}}=\mathcal{W}\ltimes(\mathfrak{g}\otimes \mathcal{A})\oplus \mathbb{C}C$, where $\mathcal{A}=\mathbb{C}[t^{\pm…

In previews works, joint with N. Gurevitch, a family of Rankin-Selberg integrals were shown to represent the twisted standard $\mathcal{L}$-function $\mathcal{L}\left(s,\pi,\chi,\mathfrak{st}\right)$ of a cuspidal representation $ \pi$ of…

In this paper, we derive improved a priori error estimates for families of hybridizable interior penalty discontinuous Galerkin (H-IP) methods using a variable penalty for second-order elliptic problems. The strategy is to use a…

The $P = W$ conjecture identifies the perverse filtration of the Hitchin system on the cohomology of the moduli space of Higgs bundles with the weight filtration of the corresponding character variety. In this paper, we introduce an…

When $G_{\mathbb{R}}$ is a real, linear algebraic group, the orbit method predicts that nearly all of the unitary dual of $G_{\mathbb{R}}$ consists of representations naturally associated to orbital parameters $(\mathcal{O},\Gamma)$. If…

Let $W$ be a finite-dimensional representation of a reductive algebraic group $G$. The invariant Hilbert scheme $\mathcal{H}$ is a moduli space that classifies the $G$-stable closed subschemes $Z$ of $W$ such that the affine algebra $k[Z]$…

Let $G$ be a simply connected, connected completely solvable Lie group with Lie algebra $\mathfrak{g}=\mathfrak{p}+\mathfrak{m}.$ Next, let $\pi$ be an infinite-dimensional unitary irreducible representation of $G$ obtained by inducing a…

We define the Higgs algebra $\mathcal{H}_\P1$ of the projective line, as a convolution algebra of constructible functions on the global nilpotent cone $\underline{\Lambda}_\P1$, a lagrangian substack of the Higgs bundle $T^*\Coh_\P1$, where…

For a semisimple Lie group $G$ satisfying the equal rank condition, the most basic family of unitary irreducible representations is the Discrete Series found by Harish-Chandra. In this paper, we continue our study of the branching laws for…

Let W be a complex reflection group and H_c(W) the Rational Cherednik algebra for $W$ depending on a parameter c. One can consider the category O for H_c(W). We prove a conjecture of Rouquier that the categories O for H_c(W) and H_{c'}(W)…

Let $\mu$ be the Haar measure of a unimodular locally compact group $G$ and $m (G)$ as the infimum of the volumes of all open subgroups of $G$. The main result of this paper is that \begin{align*} \int_{G}^{} f \circ \left( \phi_1 * \phi_2…

Let W be a real symplectic space and (G,G') an irreducible dual pair in Sp(W), in the sense of Howe, with G compact. Let $\widetilde{\mathrm{G}}$ be the preimage of G in the metaplectic group $\widetilde{\mathrm{Sp}}(\mathrm{W})$. Given an…

Let $\pi$ and $\pi'$ be unitary cuspidal automorphic representations of $\mathrm{GL}(n)$ and $\mathrm{GL}(n')$ over a number field $F$. We establish a new zero-free region for all $\mathrm{GL}(1)$-twists of the Rankin-Selberg $L$-function…

The Gutzwiller semiclassical trace formula links the eigenvalues of the Scrodinger operator ^H with the closed orbits of the corresponding classical mechanical system, associated with the Hamiltonian H, when the Planck constant is small…

Let $\pi_1,\ldots,\pi_k$ be smooth irreducible representations of $p$-adic general linear groups. We prove that the parabolic induction product $\pi_1\times\cdots\times \pi_k$ has a unique irreducible quotient whose Langlands parameter is…

Let $\mathbf{G}$ be a connected reductive algebraic group over a $p$-adic local field $F$. In this paper we study the asymptotic behaviour of the trace characters $\theta _{\pi}$ evaluated at a regular element $\gamma $ of $\mathbf{G}(F)$…

In this paper, we contribute to the broad aim of relating invariants of additive and monoidal categorifications of cluster algebras. Specifically, in the setting of representations of a quantum affine algebra $U_q'(\mathfrak{g})$,…