Related papers: $\mathcal{L}$-invariant for Siegel-Hilbert forms

In 2010, V. Futorny and S. Ovsienko gave a realization of $U(\mathfrak{gl}_n)$ as a subalgebra of the ring of invariants of a certain noncommutative ring with respect to the action of $S_1\times S_2\times\cdots\times S_n$, where $S_j$ is…

We consider the possible covariant external algebra structures for Cartan's 1-forms on GL_q(N) and SL_q(N). We base upon the following natural postulates: 1. the invariant 1-forms realize an adjoint representation of quantum group; 2. all…

A number field $K$ is Hilbert-Speiser if all of its tame abelian extensions $L/K$ admit NIB (normal integral basis). It is known that $\mathbb{Q}$ is the only such field, but when we restrict $\text{Gal}(L/K)$ to be a given group $G$, the…

We construct small parabolic eigenvarieties for holomorphic Siegel cuspforms of genus $2$ and study families of Galois representations attached to them in the spirit of Bella\"iche--Chenevier. In the course, we introduce the notion of…

Let $\rho: SL(2,\mathbb{Z})\to GL(2,\mathbb{C})$ be an irreducible representation of the modular group such that $\rho(T)$ has finite order $N$. We study holomorphic vector-valued modular forms $F(\tau)$ of integral weight associated to…

The goal of this paper is to remove the irreducibility hypothesis in a theorem of Richard Taylor describing the image of complex conjugations by $p$-adic Galois representations associated with regular, algebraic, essentially self-dual,…

Consider the semisimple mod p reduction of the Galois representation associated to a Hilbert newform f by Carayol and Taylor. This paper discusses how, under certain conditions on f, the universal ring for deformations of this residual…

We prove an explicit integral representation -- involving the pullback of a suitable Siegel Eisenstein series -- for the twisted standard $L$-function associated to a holomorphic vector-valued Siegel cusp form of degree $n$ and arbitrary…

Let (N, G), where N is a normal subgroup of G<SL_n(C), be a pair of finite groups and V a finite-dimensional fundamental G-module. We study the G-invariants in the symmetric algebra S(V) by giving explicit formulas of the Poincar\'{e}…

We introduce invariants of Hurwitz equivalence classes with respect to arbitrary group $G$. The invariants are constructed from any right $G$-modules $M$ and any $G$-invariant bilinear function on $M$, and are of bilinear forms. For…

We present and discuss an algorithm and its implementation that is capable of directly determining Fourier expansions of any vector-valued modular form of weight at least $2$ associated with representations whose kernel is a congruence…

In recent work, the authors proved a general result on lifting $G$-irreducible odd Galois representations $\mathrm{Gal}(\overline{F}/F) \to G(\overline{\mathbb{F}}_{\ell})$, with $F$ a totally real number field and $G$ a reductive group, to…

For a semisimple, simply-connected linear algebraic group, $G$, and parabolic subgroup, $P\subseteq G$, we use the fact that the Hilbert polynomial of the equivariant embedding of $G/P$ is equal to the Hilbert function to compute an…

Consider a family of modular forms of weight 2, all of whose residual $\pmod{p}$ Galois representations are isomorphic. It is well-known that their corresponding Iwasawa $\lambda$-invariants may vary. In this paper, we study this variation…

We prove a comparison theorem between Greenberg--Benois $\mathcal{L}$-invariants and Fontaine--Mazur $\mathcal{L}$-invariants. Such a comparison theorem supplies an affirmative answer to a speculation of Besser--de Shalit.

We state and prove a formula for a certain value of the Goss L-function of a Drinfeld module. This gives characteristic-p-valued function field analogues of the class number formula and of the Birch and Swinnerton-Dyer conjecture. The…

In these paper we compute Jordan-Kronecker invariants of Lie algebra representations, introduced earlier by A.V. Bolsinov, A.M. Izosimov and I.K. Kozlov, for a number of representations. In particular, we compute them for the sums of…

Galilei invariant equations for massive fields with various spins are found and classified. They have been obtained directly, i.e., by using requirement of Galilei invariance and the facts on representations of the Galilei group deduced in…

A strong version of the quantization conjecture of Guillemin and Sternberg is proved. For a reductive group action on a smooth, compact, polarized variety (X,L), the cohomologies of L over the GIT quotient X // G equal the invariant part of…

Let F be a non-Archimedean locally compact field of residue characteristic p, let G be an inner form of GL(n,F) with n>0, and let l be a prime number different from p. We describe the block decomposition of the category of finite length…