Related papers: Supercuspidal representations: construction, class…

The construction approach proposed in the previous paper Ref. 1 allows us there and in the present paper to construct at generic deformation parameter $q$ all finite--dimensional representations of the quantum Lie superalgebra…

In this paper, we introduce a representation theory of Hom-Lie conformal superalgebras and discuss the cases of adjoint representations. Furthermore, we develop cohomology theory of Hom-Lie conformal superalgebras and discuss some…

In the present paper, we will show that three apparently disjoint objects: Galois representations arising from twenty-seven lines on a cubic surface (number theory and arithmetic algebraic geometry), Picard modular forms (automorphic…

Let G be a classical p-adic group and $(\psi ,\epsilon)$ the Langlands parameter of an irreducible supercuspidal representation of a Levi subgroup of G. Using data from $(\psi ,\epsilon)$, we determine explicitly the intertwining algebra of…

We show that the categories of smooth ${\rm SL}_2({\mathbb Q}_p)$-representations (resp. ${\rm GL}_2({\mathbb Q}_p)$-representations) of level $1$ on $p$-torsion modules are equivalent with certain explicitly described equivariant…

Finite and Infinite-dimensional representations of symmetry algebras play a significant role in determining the spectral properties of physical Hamiltonians. In this paper, we introduce and apply a practical method to construct infinite…

Using Butz and Moerdijk's topological groupoid representation of a topos with enough points, a `syntax-semantics' duality for geometric theories is constructed. The emphasis is on a logical presentation, starting with a description of the…

Existing machine learning frameworks operate over the field of real numbers ($\mathbb{R}$) and learn representations in real (Euclidean or Hilbert) vector spaces (e.g., $\mathbb{R}^d$). Their underlying geometric properties align well with…

The article is devoted to some ``strange'' phenomena of representation theory and their interrelations. Cross-projective representations of pairs of anticommutative algebras, alloys, their universal envelopping Lie algebras and their…

We prove the formal degree conjecture for simple supercuspidal representations of symplectic groups and quasi-split even special orthogonal groups over a p-adic field, under the assumption that p is odd. The essential part is to compute the…

We study representations of the classical infinite dimensional real simple Lie groups $G$ induced from factor representations of minimal parabolic subgroups $P$. This makes strong use of the recently developed structure theory for those…

In this paper we will derive an explicit description of the genuine projective representations of the symmetric group $S_n$ using Dirac cohomology and the branching graph for the irreducible genuine projective representations of $S_n$. In…

We study multiplicative Dirac structures on Lie groups. We show that the characteristic foliation of a multiplicative Dirac structure is given by the cosets of a normal Lie subgroup and, whenever this subgroup is closed, the leaf space…

Given a Lie superalgebra \g, we introduce several variants of the representation ring, built as subrings and quotients of the ring R_{\Z_2}(\g) of virtual \g-supermodules (up to even isomorphisms). In particular, we consider the ideal…

Let $D$ be the quatenion division algebra over a non-Archimedean local field $F$ of characteristic zero and odd residual characterisitc. We show that an irreducible discrete series representation of $\mathrm{GL}_n(D)$ is…

We define a new notion of cuspidality for representations of $\GL_n$ over a finite quotient $\Oh_k$ of the ring of integers $\Oh$ of a non-Archimedean local field $F$ using geometric and infinitesimal induction functors, which involve…

We introduce a new way to study representations of the Lie superalgebra $p(n)$. Since the center of the universal enveloping algebra $U$ acts trivially on all irreducible representations, we suggest to study the quotient algebra $\bar{U}$…

Take S to be a 4-dimensional Sklyanin (elliptic) algebra that is module-finite over its center Z; thus, S is PI. Our first result is the construction of a Poisson Z-order structure on S such that the induced Poisson bracket on Z is…

We construct all finite irreducible modules over Lie conformal superalgebras of type W and S.

In this paper we investigate the theory of cuspidalisation of sections of arithmetic fundamental groups of hyperbolic curves to cuspidally i-th and 2/p-th step prosolvable arithmetic fundamental groups. As a consequence we exhibit two,…