Related papers: Shintani functions, real spherical manifolds, and …

Let Sp_V(F) be the group of isometries of a symplectic vector space V over a finite field F of odd cardinality. The group Sp_V(F) possesses distinguished representations--- the Weil representations. We know that they are compatible with…

Let $(G,G_1)=(G,(G^\sigma)_0)$ be a symmetric pair of holomorphic type, and we consider a pair of Hermitian symmetric spaces $D_1=G_1/K_1\subset D=G/K$, realized as bounded symmetric domains in complex vector spaces ${\mathfrak…

Let F be either R or C. Let $(\pi,V)$ be an irreducible admissible smooth \Fre representation of GL(2n,F). A Shalika functional $\phi:V \to \C$ is a continuous linear functional such that for any $g\in GL_n(F), A \in \Mat_{n \times n}(F)$…

We introduce the multiple zeta functions with structures similar to those of symmetric functions such as Schur $P$-, Schur $Q$-, symplectic and orthogonal functions in the representation theory. We first consider their basic properties such…

A collection of infinite dimensional complete vector fields $\left\{V_i\right\}_{i=1}^{\infty}$ acting on a locally convex manifolds $M$ on which a smooth positive measure $\mu$ is defined was considered. It was assumed that the vector…

The operator, $\chi $, of weak commutativity between isomorphic groups $G$ and $G^{\varphi }$ was introduced by Sidki as \begin{equation*} \chi (G)=\left\langle G \cup G^{\varphi }\mid \lbrack g,g^{\varphi }]=1\,\forall \,g\in…

Let $E/F$ be a quadratic extension of fields, and $G$ a connected quasi-split reductive group over $F$. Let $G^{op}$ be the opposition group obtained by twisting $G$ by the duality involution considered by Prasad. Assume that the field $F$…

The rational Cherednik algebra $\HH$ is a certain algebra of differential-reflection operators attached to a complex reflection group $W$. Each irreducible representation $S^\lambda$ of $W$ corresponds to a standard module $M(\lambda)$ for…

We state and prove a corrected version of a theorem of Singerman, which relates the existence of symmetries (anticonformal involutions) of a quasiplatonic Riemann surface $\mathcal S$ (one uniformised by a normal subgroup $N$ of finite…

Let $A$ be abelian variety over the function field $K$ of a compact Riemann surface $B$. Fix a model $f \colon \mathcal{A} \to B$ of $A/K$ and a certain effective horizontal divisor $\DD \subset \mathcal{A}$. We give a sufficient condition…

We address a question from \cite{BKV25} regarding the finiteness of the homological $R$-isoperimetric function. Let $R$ be a subfield of the complex numbers $\mathbb{C}$ with the absolute value norm. We prove that for any group $G$ that…

We study the class $\mathcal C$ of symmetric functions whose coefficients in the Schur basis can be described by generating functions for sets of tableaux with fixed shape. Included in this class are the Hall-Littlewood polynomials,…

We consider the partition function Z(N;x_1,...,x_N,y_1,...,y_N) of the square ice model with domain wall boundary. We give a simple proof of the symmetry of Z with respect to all its variables when the global parameter a of the model is set…

We derive new results on the characterization of Gelfand--Shilov spaces $\mathcal{S}^\mu_\nu (\R^n)$, $\mu,\nu >0$, $\mu+\nu \geq 1$ by Gevrey estimates of the $L^2$ norms of iterates of $(m,k)$ anisotropic globally elliptic Shubin (or…

We consider irreducible unitary representations $A_i$ of G=SO(n+1,1) with the same infinitesimal character as the trivial representation and representations $B_j$ of H=SO(n,1) with the same properties and discuss H-equivariant homomorphisms…

Petrie symmetric functions $G(k,n)$, also known as truncated homogeneous symmetric functions or modular complete symmetric functions, form a class of symmetric functions interpolating between the elementary symmetric functions $e_n$ and the…

Recent developments in particle physics have revealed deep connections between scattering amplitudes and tropical geometry. From the heart of this relationship emerged the chirotropical Grassmannian $\text{Trop}^\chi \text{G}(k,n)$ and the…

We give a partial super analog of a result obtained by S. Sahi and G. Zhang relating Shimura operators and certain interpolation symmetric polynomials. In particular, we study the pair $(\mathfrak{gl}(2p|2q),…

We study the size of the isometry group Isom(M, g) of Riemannian manifolds (M, g) as g varies. For M not admitting a circle action, we show that the order of Isom(M, g) can be universally bounded in terms of the bounds on Ricci curvature,…

Let $\Gamma$ be a finite group. Consider the wreath product $G_n := \Gamma^n \rtimes S_n$ and the subgroup $K_n := \Delta_n \times S_n\subseteq G_n$, where $S_n$ is the symmetric group and $\Delta_n$ is the diagonal subgroup of $\Gamma^n$.…